The moduli space of genus 4 even spin curves is rational
Hiromichi Takagi, Francesco Zucconi
利用三重Mori理论的技巧，证明了以亏格为4的平滑曲线和整体瓣为零的半标准因子为参数的一般点的模空间是有理的.
By the technique of 3-fold Mori theory, we prove that the moduli space whose general point parameterizes a couple of a smooth curve of genus 4 and a halfcanonical divisor with vanishing global section is rational.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The unirationality of the moduli space of curves of genus $\leq 14$
新的结果是亏格为14的曲线的模空间的单合理性。该方法适用于低级属。
The rationality of the moduli spaces of trigonal curves of odd genus
证明了奇亏格$g>4$三角曲线的模空间是有理的。
We study the induced Ekedahl-Oort stratification on the moduli of curves of genus 4 in positive characteristic.
Extremal effective divisors on the moduli space of n-pointed genus one curves
对于每一个$n\geq 3$，我们在亏格为1的曲线的模空间上展示了无穷多个带有$n$标记点的极值有效因子。
Pryms of non-cyclic triple coverings and log canonical models of the spin moduli space of genus 2
利用Prym映射证明了亏格为2的曲线的非三重循环覆盖的模空间与亏格为2的偶自旋曲线的非三重循环覆盖的模空间是双有理同构的.本文描述亏格为2的偶自旋曲线的模空间的对数正则模型，并利用它推广了上述双有理映射。
The moduli of curves of genus 6 and K3 surfaces
通过对某些格极化K3曲面的模空间给出周期映射，证明亏格为6的曲线的粗模空间对于IV型有界对称整环的算术商是双有理的.
Towards the cohomology of moduli spaces of higher genus stable maps
本文证明了Vakil和Zinger最近构造的亏格g = 1的稳定映射的模空间的轨道化在奇数次k < 10时具有零有理上同调群.
On the Kodaira dimension of the moduli space of curves of genus 16
本文证明了亏格16曲线模空间不是一般型，解决了该维数下的一个长期未决问题。
Given a collection of boundary divisors in the moduli space of stable genus-zero n-pointed curves, Giansiracusa proved that their intersection is nonempty if and only if all pairwise intersections are nonempty. We give a complete classification of the pairs (g,n) for which the analogous statement holds in the moduli space of n-pointed curves of genus g.
We compute the rational cohomology of the moduli space of trigonal curves of genus 5. We do this by considering their natural embedding in the first Hirzebruch surface and by using Gorinov-Vassiliev's method.
The global geometry of the moduli spaces of higher spin curves and their birational classification is largely unknown for g >= 2 and r > 2. Using quite related geometric constructions, we almost complete the picture of the known results in genus g <= 4 showing the rationality of the moduli spaces of even and odd 4-spin curves of genus 3, of odd spin curves of genus 4 and of 3-spin curves of genus 4.
We compute cohomology of the moduli space of genus three curves with level two structure and some related spaces. In particular, we determine the cohomology groups of the moduli space of plane quartics with level two structure as representations of the symplectic group on a six dimensional vector space over the field of two elements. We also make the analogous computations for some related spaces such as moduli spaces of genus three curves with a marked points and strata of the moduli space of Abelian differentials of genus three.
Quantum cohomology of moduli spaces of genus zero stable curves
研究亏格为0的稳定n点曲线的模空间的（小）量子上同调环。特别是，我们确定了一个明确的介绍，在n=5的情况下，我们概述了计算方法的情况下n=6。
Cohomology of moduli spaces of curves of genus three via point counts
本文研究亏格为3的光滑$n$ -点非超椭圆曲线的模空间。为了寻求这个空间的上同调信息，我们对$n \leq 7$在有限域上定义的点的个数作了$\mathbb{S}_n$ -等变计数.结合亏格为0、1、2的光滑尖曲线的模空间和亏格为3的光滑超椭圆曲线的模空间的结果，我们可以确定的$\mathbb{S}_n$ -等变伽罗瓦和霍奇结构的$n \leq 5$亏格为3的稳定曲线的模空间的（$\ell$ -adic或Betti）上同调（为了获得$n \leq 7$，我们需要“亏格2的8点曲线”的计数）。
The moduli space of curves of genus 16 is uniruled
该研究运用非阿贝尔布里尔-诺特理论，证明16亏格曲线的模空间是单有理的，这是目前已知该类结果的最高亏格。
Weil-Petersson volumes of moduli spaces of curves and the genus expansion in two dimensional gravity
得到了一个与二维引力中自由能亏格展开式相同的尖曲线模空间的Weil-Petersson体积母函数公式。任意亏格的贡献用贝塞尔函数$J_0$表示。
Chow ring of moduli spaces of quasi-polarised K3 surfaces in lower genus
本文研究低亏格拟极化 K3 曲面模空间，证明亏格不超过 5 时其周环由重言类构成。
We construct a smooth Artin stack parameterizing the stable weighted curves of genus one with twisted fields and prove that it is isomorphic to the blowup stack of the moduli of genus one weighted curves studied by Hu and Li. This leads to a blowup-free construction of Vakil-Zinger's desingularization of the moduli of genus one stable maps to projective spaces. This construction provides the cornerstone of the theory of stacks with twisted fields, which is thoroughly studied in arXiv:2005.03384 and leads to a blowup-free resolution of the stable map moduli of genus two.
A complete curve of genus 5 in the moduli space of curves of genus 3 and related questions
研究复数域上亏格3曲线模空间，通过特定方法证明其中存在一条亏格105的完备曲线。
A geometry of the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one
本文利用希钦映射和椭圆曲线希格斯丛模空间的平坦退化，刻画了算术亏格为一的不可约节点曲线上希格斯对模空间的几何结构。
We study the moduli space of stable sheaves of Euler characteristic 2, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers and we give a classification of the stable sheaves involving locally free resolutions.
The moduli space of étale double covers of genus 5 curves is unirational
证明了亏格为5的曲线在复数上的双覆盖的粗模空间$\cR_5$是单有理的.我们给出了两个略有不同的参数，一个纯粹的几何和其他更多的计算。
Using the connection discovered by Hassett between the Noether-Lefschetz moduli space of special cubic fourfolds of discriminant 42 and the moduli space F_{22} of polarized K3 surfaces of genus 22, we show that the universal K3 surface over F_{22} is unirational.
The Dimension of the Moduli Space of Pointed Algebraic Curves of Low Genus
本文针对亏格不超过7的多种情形，显式计算了以给定数值半群为Weierstrass半群的带点代数曲线的模空间，并确定了所有亏格7半群的维数。
The class of a Hurwitz divisor on the moduli of curves of even genus
在亏格为$g=2k$的稳定曲线的模空间上，计算了具有两个单分歧点的射影线的度$k+1$覆盖所给出的Hurwitz因子$D_2$的循环类.我们还研究了$k+1$和$2k$度容许覆盖的Hurwitz空间到亏格$2k$稳定曲线的模空间的自然映射的几何性质.
We study here the tautological rings of the moduli spaces of compact Riemann surfaces of genus 1,2,3 and 4 with marked points. The paper presents the complete descriptions of these rings by describing the groups of all degrees.
The stringy E function of the moduli space of rank 2 bundles over a Riemann surface of genus 3
计算亏格为3的黎曼曲面上秩为2的丛的模空间的弦E函数。在这样做的时候，我们回答了Batyrev的一个问题，关于GIT线性表示的弦E函数。
On Deformations and Moduli of Genus 2 Fibrations
本文研究了具有亏格为2的纤维化的一般型曲面的模，其中g_b >= 2是基的亏格，q = g_b + 1.我们证明了光滑纤维化是由模空间中的唯一分量参数化的。同样的结果也适用于具有特殊g_b值的非光滑纤维化。在一般情况下，我们给出了相应连通分支维数的一个界。
The rationality of the moduli space of curves of genus 3 after P. Katsylo
本文综述了Katsylo关于亏格为3的光滑射影复曲线的模空间是有理的证明。我们希望通过强调证明中的潜在几何及其关键结构特征，使论证更易于理解和透明。
Moduli of Genus Six Curves and K-stability
本文研究亏格六曲线的K-模空间，通过显式描述五次对数Fano对的穿墙结构对其层进行分类，并揭示K-模空间在GIT模空间与K3曲面模空间之间的插值关系。
We study the moduli space of stable sheaves of Euler characteristic 1, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We give a classification of the stable sheaves involving locally free resolutions or extensions. We compute the Betti numbers by studying the variation of the moduli spaces of alpha-semi-stable pairs.
Heegner divisors in the moduli space of genus three curves
S.近藤用$K3$曲面的周期证明了亏格为3的曲线的模空间对于一个复6-球的算术商是双有理的。本文研究了球商中的Heegner因子，它由球的算术定义的超平面截面给出。证明了亏格为三的曲线的对应轨迹为：超椭圆曲线，奇异平面四次曲线和允许某些有理“分裂曲线”的平面四次曲线。
The uniruledness of the Prym moduli space of genus 9
本文证明亏格 9 的 Prym 曲线模空间 R_9 单有理性，并指出这是 R_g 具有负 Kodaira 维数的最大亏格。
Towards large genus asymtotics of intersection numbers on moduli spaces of curves
我们显式地计算了$n$ -尖复代数曲线的模空间的Weil-Petersson体积的大亏格渐近中的发散因子。模一个普遍的乘法常数，我们证明了一个完整的渐近展开的Weil-Petersson体积的逆幂的属的系数是多项式在$n$。这是通过分析更一般的重言式类的相交数的各种递归来完成的，重言式类的大亏格渐近行为也被广泛研究。
We prove that the moduli space of polarized $K3$ surfaces of genus eleven with $n$ marked points is unirational when $n\leq 6$ and uniruled when $n\leq7$. As a consequence, we settle a long standing but not proved assertion about the unirationality of $\cal{M}_{11,n}$ for $n\leq6$. We also prove that the moduli space of polarized $K3$ surfaces of genus eleven with $9$ marked points has non-negative Kodaira dimension.
We compute the Picard group of the moduli stack of smooth curves of genus $g$ for $3\leq g\leq 5$, using methods of equivariant intersection theory. We base our proof on the computation of some relations in the integral Chow ring of certain moduli stacks of smooth complete intersections. As a byproduct, we compute the cycle classes of some divisors on $\mathcal{M}_g$.
Birational contraction of genus two tails in the moduli space of genus four curves I
我们证明了对于$α\in (2/3, 7/10)$，$(\bar M_4, αδ)$对的对数正则模型$\bar M_4(α)$同构于h-半稳定曲线的模空间$\bar M_4^{hs}$，并且存在一个双有理态射$Ξ: \bar M_4^{hs} \to \bar M_4(2/3)$，它收缩了曲线$C_1\cup_p C_2$的轨迹，该曲线由两条相交于节点$p$的亏格曲线组成，使得$p$是$C_1$或$C_2$的Weierstrass点.为了得到这个态射，我们构造了一个紧致的模空间$\bar M_{2,1}^{hs}$，它是由两条以结点、普通尖点和带结点为奇点的点亏格的曲线构成的，并证明了它与Rulla在他的论文中构造的翻转是同构的.
Classical and minimal models of the moduli space of curves of genus two
本文讨论对数极小模型程序在曲线的模空间中的应用，特别是在亏格为2的曲线的情况下。这些模空间的对数正则模型通常可以使用几何不变理论的技术来构造。在第二类中，这归结为二元六分仪的不变量理论，它在19世纪得到了系统的发展。
We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of bidegree (3, 3) contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of alpha-semi-stable pairs.
The Geometry of the Moduli Space of Curves of Genus 23
我们证明亏格23的曲线的模空间M_{23}的Kodaira维度至少为2。我们还提出了一些证据的假设，Kodaira维数的模空间实际上是等于2。注意，当g > 23时，模空间是一般类型的，而当g为\leq 22时，Harris和Morrison证明M_g是uniruled的。通过研究三个Brill-Noether型显式多正则因子的相对位置，得到了关于M_{23}的结果.
On the Fields of Moduli of Curves of Genus Six
研究亏格为六的曲线的模域问题，通过考虑模空间\(M_6\)的分层，探讨曲线在其模域上有模型的条件。
Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces
本文研究低次数光滑超曲面上高亏格曲线映射模空间的奇异性，证明次数相对亏格足够大时模空间奇异，并给出奇异轨迹维数下界。
An Invitation to the Local Structures of Moduli of Genus one stable maps
本文提供了一些初等例子来证明文[1]关于亏格为1的稳定映射到射影空间的模空间的局部结构结果。希望这些例子对研究生学习这一重要学科有所帮助。
This is the second in a pair of papers developing a framework to apply logarithmic methods in the study of singular curves of genus $1$. This volume focuses on logarithmic Gromov--Witten theory and tropical geometry. We construct a logarithmically nonsingular moduli space of genus $1$ curves mapping to any toric variety. The space is a birational modification of the principal component of the Abramovich--Chen--Gross--Siebert space of logarithmic stable maps and produces an enumerative genus $1$ curve counting theory. We describe the non-archimedean analytic skeleton of this moduli space and, a…
The rationality of certain moduli spaces of curves of genus 3
对于每个代数闭域，我们证明了以下两个模空间的合理性：M（3，3）个参数化对（C，η），其中C的亏格为3，η是M（3，）<3>个参数化对（C，<η>）的3-扭除子类，其中<η>是由η生成的Pic_0（C）中的3阶循环子群.
Tropical geometry is a relatively recent field in mathematics created as a simplified model for certain problems in algebraic geometry. We introduce the definition of abstract and planar tropical curves as well as their properties, including combinatorial type and degree. We also talk about the moduli space, a geometric object that parameterizes all possible types of abstract or planar tropical curves subject to certain conditions. Our research focuses on the moduli spaces of planar tropical curves of genus one, arbitrary degree d and any number of marked, unbounded edges. We prove that these …
The final log canonical model of the moduli space of stable curves of genus four
我们描述了亏格为4的稳定曲线的模空间的最终对数正则模型。我们证明了从$\bar{M}_4$到这个模型的有理映射收缩了Petri和边界因子，翻转了超椭圆轨迹。作为应用，我们得到了$\bar{M}_4$上移动因子斜率的一个精确界。
K-stability of Thaddeus' moduli of stable bundle pairs on genus two curves
本文研究了Thaddeus稳定束对模空间的K-稳定性，证明其与四次del Pezzo三次型中的线的GIT模空间同构，并建立了与稳定向量包模空间的自然映射。
We compute the intersection Betti numbers of the GIT model of the moduli space of Brill-Noether-Petri general curves of genus 4. This space was shown to be the final non-trivial log canonical model for the moduli space of stable genus four curves, under the Hassett-Keel program. The strategy of the cohomological computation relies on a general method developed by Kirwan to calculate the cohomology of GIT quotients of projective varieties, based on the equivariantly perfect stratification of the unstable points studied by Hesselink and others and a partial resolution of singularities.
The Euler characteristic of local systems on the moduli of genus 3 hyperelliptic curves
对于非负整数的划分$lambda=\{lambda_1 \geq λ_2 \geq λ_3 \}$，通过适当的分层，计算了亏格为3的超椭圆曲线的模空间上局部系统$V_λ$的欧拉示性数.对于某些低次$λ$，利用有限域上曲线的计数，对$V_λ$的运动欧拉示性数作了一个猜想.
Moduli of rank 4 symplectic bundles over a curve of genus 2
设X是亏格为2的光滑不可约复射影曲线。X上秩为4的半稳定辛向量丛的模空间M_2是一个维数为10的簇。在综合了X上秩为2的奇次向量丛的一些结果之后，我们利用一族5维射影空间构造了M_2的一般有限覆盖，并给出了一些应用。
On The Moduli of Surfaces Admitting Genus Two Fibrations Over Elliptic Curves
本文研究了椭圆曲线上亏格为二纤维化的复射影曲面的结构、变形和模空间。我们观察到，一个表面承认一个光滑纤维化，如上述是椭圆形的，我们采用的结果，极化椭圆表面的模，以构建这些光滑纤维化的模空间。在非光滑纤维化的情况下，我们将模空间与从椭圆曲线到模曲线$X(d)$，$d\geq 3$的度$n$的态射的Hurwitz方案${\cal H}(1,X(d),n)$联系起来。最后，我们表明，模空间在非光滑的情况下，纤维空间的仿射线${\mathbb A}^1$与纤维确定的组件的${\cal H}(1,X(d),n)$。
The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for degree coprime to n)
基于我们之前与A. Schmitt [7]我们解释了一个递归算法，以确定任何给定曲线上的希格斯包的模空间的上同调（在互质的情况下）。作为该方法的一个应用，我们计算了任意秩n的PGL_n-Higgs丛空间的y-亏格，证实了T.豪塞尔
This is the first in a pair of papers developing a framework for the application of logarithmic structures in the study of singular curves of genus $1$. We construct a smooth and proper moduli space dominating the main component of Kontsevich's space of stable genus $1$ maps to projective space. A variation on this theme furnishes a modular interpretation for Vakil and Zinger's famous desingularization of the Kontsevich space of maps in genus $1$. Our methods also lead to smooth and proper moduli spaces of pointed genus $1$ quasimaps to projective space. Finally, we present an application to t…
We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of alpha-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.
The Chow ring of the moduli space of curves of genus zero
在回顾了亏格为零的曲线的模空间的几种构造之后，给出了亏格为零的曲线的模空间的另一种构造。这给出了这个空间的交环的简单描述。我们给出了一个基础的周群和一个明确的对偶周群之间的互补度。有一个递归描述这个代数S。龙骨我们的介绍是简单的意义上，有更少的发电机和更少的关系，我们的描述是明确的。
On moduli of pointed real curves of genus zero
引入亏格为零的点实曲线的模空间$R \bar{M}_{2k,l}$，并给出它的自然分层。$R \bar{M}_{2k,l}$的层对应于亏格为零的实曲线，具有不同的退化类型，并由它们的对偶树进行编码。利用这种分层，我们计算了$R \bar{M}_{2k,l}$的第一Stiefel-Whitney类，并构造了定向双覆盖$R \widetilde{M}_{2k,l}$ $ of $ R \bar{M}_{2k,l} $.
We present a structure theorem for the moduli space R_7 of Prym curves of genus 7 as a projective bundle over the moduli space of 7-nodal rational curves. The existence of this parametrization implies the unirationality of R_7 and that of the moduli space of Nikulin surfaces of genus 7, as well as the rationality of the moduli space of Nikulin surfaces of genus 7 with a distinguished line. Using the results in genus 7, we then establish that R_8 is uniruled.
Moduli spaces of stable maps to a smooth projective variety typically have several components. We express the virtual class of the moduli space of genus one stable maps to a smooth projective variety as a sum of virtual classes of the components. The key ingredient is a generalised functoriality result for virtual classes. We show that the natural maps from 'ghost' components of the genus one moduli space to moduli spaces of genus zero stable maps satisfy the strong push forward property. As a consequence, we give a cycle-level formula which relates standard and reduced genus one Gromov--Witte…
Rational cohomology of the moduli spaces of pointed genus 1 curves
本文给出了亏格为1的点曲线的模空间的有理上同调的组合刻画，它具有$n$标记点和水平$N$结构.更准确地说，我们明确地描述了Leray谱序列的遗忘映射$\EuScript{M}_{1,n}(N)\to\EuScript{M}_{1,1}(N)$的$E_2$项，并表明该结果是同构的有理上同调的$\EuScript{M}_{1,n}(N)$作为一个合理的混合霍奇结构配备了一个行动的对称群$\mathfrak{S}_n$。经典模空间$\EuScript{M}_{1,n}$是N=1的特殊情况。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。