Gromov-Witten invariants for G/B and Pontryagin product for ΩK
Naichung Conan Leung, Changzheng Li
给出了G/B的（T-等变）3-点亏格零Gromov-Witten不变量的一个显式公式.我们通过找到基环群ΩK的同调上的等变Pontryagin积的一个显式公式来导出它。
We give an explicit formula for (T-equivariant) 3-pointed genus zero Gromov-Witten invariants for G/B. We derive it by finding an explicit formula for the equivariant Pontryagin product on the homology of the based loop group ΩK.
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
A projected Gromov-Witten variety is the union of all rational curves of fixed degree that meet two opposite Schubert varieties in a homogeneous space X = G/P. When X is cominuscule we prove that the map from a related Gromov-Witten variety is cohomologically trivial. This implies that all (3 point, genus zero) K-theoretic Gromov-Witten invariants of X are determined by the projected Gromov-Witten varieties, which extends an earlier result of Knutson, Lam, and Speyer. Our proof uses that any projected Gromov-Witten variety in a cominuscule space is also a projected Richardson variety.
We define the double Gromov-Witten invariants of Hirzebruch surfaces in analogy with double Hurwitz numbers, and we prove that they satisfy a piecewise polynomiality property analogous to their 1-dimensional counterpart. Furthermore we show that each polynomial piece is either even or odd, and we compute its degree. Our methods combine floor diagrams and Ehrhart theory.
Localization in Gromov-Witten Theory and Orbifold Gromov-Witten Theory
在这篇临时文章中，我们解释了如何使用本地化来计算光滑复曲面簇的Gromov-Witten不变量和光滑复曲面Deligne-Mumford栈的orbifold Gromov-Witten不变量。
Symmetries of Gromov-Witten invariants
群（Z/nZ）^2作用于复旗流形的Gromov-Witten不变量。我们还推出了这个结果的几个推论。
A Formula of the One-leg Orbifold Gromov-Witten Vertex and Gromov-Witten Invariants of the Local $\cB\bZ_m$ Gerbe
本文给出了框架单腿轨道Gromov-Witten顶点的一个公式，其中腿是各向同性群$\bZ_m$的gerby.然后利用这个公式计算局部$\cB\bZ_m$ gerbe的Gromov-Witten不变量。我们还将计算一次和二次$\bZ_2$ -Hodge积分的一些例子。
We prove some vanishing conditions on the Gromov-Witten invariants of product of P1.
The Aspinwall-Morrison calculation and Gromov-Witten theory
通过将Aspinwall-Morrison公式的计算与Gromov-Witten理论相联系，证明了Aspinwall-Morrison公式。
We derive a recursive formula for certain relative Gromov-Witten invariants with maximal tangency condition via the Witten-Dijkgraaf-Verlinde-Verlinde equation. For certain relative pairs, we get explicit formulae of invariants using the recursive formula.
Gromov-Witten invariants have been constructed to be deformation invariant, but their behavior under other transformations is subtle. In this note we show that logarithmic Gromov-Witten invariants are also invariant under appropriately defined logarithmic modifications.
Gromov-Witten invariants of stable maps with fields
我们构造了带域的$\Pf$的稳定态射模的Gromov-Witten不变量.这是Guffin-Sharpe-Witten模型的全亏格数学理论，是$\Pf$的扭曲Gromov-Witten不变量的修正。这些不变量是使用Kiem-Li的余割局部化构造的，Kiem-Li是Landau-Ginzburg理论中Witten扰动方程的代数几何模拟。我们证明，这些不变量相吻合，签署，与五次的Gromov-Witten不变量。
We prove that genus zero Gromov--Witten invariants of a smooth scheme relative to a smooth divisor coincide with genus zero orbifold Gromov--Witten invariants of an appropriate root stack construction along the divisor.
In this article, we study the change of genus zero Gromov-Witten invariants under Type II extremal transitions in degree 4.
Theta functions were defined for varieties with effective anticanonical divisor and are related to certain punctured Gromov-Witten invariants. In this paper we show that in the case of a log Calabi-Yau surface (X,D) with smooth very ample anticanonical divisor we can circumvent the notion of punctured Gromov-Witten invariants and relate theta functions and their multiplicative structure to certain 2-marked log Gromov-Witten invariants. This is a natural extension of the correspondence between wall functions and 1-marked log Gromov-Witten invariants.
Notes on axiomatic Gromov--Witten theory and applications
这是一篇关于Givental的公理化Gromov-Witten理论及其应用的简要文章.
Minimal Gromov--Witten ring
我们建立了量子极小Fano簇（一个极小自然（相对于Gromov-Witten理论）簇类）的格0的Gromov-Witten不变量的抽象理论。特别地，我们考虑“最小Gromov-Witten环”，即。e.一种交换代数，其生成元和关系的形式用在Fano簇的Gromov-Witten理论中。任何量子极小簇的Gromov-Witten理论都是这个环到$\mathbb C$的同态。我们证明了抽象重构定理，该定理描述了该环与由"素两点不变量"生成的自由交换环的特殊同构。我们还找到了DN型微分方程的解决方案，为一个Fano簇的维数N的生成系列的单点Gromov-Witten不变量。
We discuss some questions about Gromov-Witten classes of target stacks.
We use Pixton's relations to prove a reconstruction theorem for genus 2 Gromov-Witten invariants in the style of Kontsevich-Manin (genus 0) and Getzler (genus 1). We also calculate genus 2 (descendant) Gromov-Witten invariants of $\mathbb{P}^2$ blown up at a finite number of points in general position.
Evidence for the Gromov-Witten/Donaldson-Thomas Correspondence
研究了曲线上$\mathbf{P}^2$ -丛的等变Gromov-Witten和Donaldson-Thomas理论.我们证明了等变GW/DT对应对于某些曲线类是一阶的
We give a summation over graphs type formula for the permutation-equivariant K-theoretic Gromov-Witten total potential of a projective manifold X in terms of cohomological Gromov-Witten (GW) invariants of X. We achieve this by describing combinatorially the Kawasaki strata of the moduli spaces of stable maps to X.
Degenerations of surface scrolls and the Gromov-Witten invariants of Grassmannians
我们描述了一种算法，用于计算某些示性数的表面涡卷使用退化。作为推论，我们得到一个方法来计算相应的Gromov-Witten不变量的格拉斯曼。
Splitting and loop theorems in logarithmic Gromov--Witten theory
该研究定义了含负接触阶的新型对数Gromov-Witten不变量理论，证明其满足对数双有理不变性及推广经典对应定理的环、分裂定理。
Gromov-Witten theory, Hurwitz theory, and completed cycles
我们建立了一个明确的等价性之间的固定部门的Gromov-Witten理论的目标曲线X和计数的Hurwitz覆盖的基础上完成的循环。根据定义，固定扇区由点类的后代形成。在移位对称函数理论中，完全循环自然出现。利用这个等价性，我们给出了射影直线和椭圆曲线的平稳Gromov-Witten理论的完整描述。导出了射影直线相对平稳理论的Toda方程。
Three questions in Gromov-Witten theory
这篇文章伴随着我在2002年8月的ICM演讲。讨论了Gromov-Witten理论的三个方向：Gorenstein性质、BPS态和Virasoro约束。每一个都指向这个主题中尚未被理解的基本结构。
We extend the definition of relative Gromov--Witten invariants with negative contact orders to all genera. Then we show that relative Gromov--Witten theory forms a partial CohFT. Some cycle relations on the moduli space of stable maps are also proved.
Absolute and relative Gromov-Witten invariants of very ample hypersurfaces
对于任意光滑复射影簇X和X中的光滑非常充裕超曲面Y，我们用代数几何的方法给出了Y在X中亏格为零的相对Gromov-Witten不变量的技巧.我们证明了相对稳定映射模空间的Chow群中的圈的一个等式，它将这些相对不变式与X和Y的Gromov-Witten不变量联系起来.给定X的Gromov-Witten不变量，我们证明了这些关系足以计算X诱导的Y的所有相对不变式以及所有亏格为零的Gromov-Witten不变量.
The Gromov-Witten and Donaldson-Thomas correspondence for trivial elliptic fibrations
本文研究了文献[MNOP 1，MNOP 2]中关于平凡椭圆纤维化的Gromov-Witten和Donaldson-Thomas对应.特别地，我们证明了当三重为$E \times S$时，准素场的Gromov-Witten和Donaldson-Thomas对应，其中$E$是光滑椭圆曲线，$S$是具有数值平凡正则类的光滑曲面.
Splitting of Gromov-Witten Invariants with Toric Gluing Strata
本文证明了在粘合分层为环面簇的假设下，可由不可约分支的穿孔Gromov-Witten不变量重构简单正规交叉簇的对数Gromov-Witten不变量的分裂公式。
We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.
Topological recursion relations and Gromov-Witten invariants in higher genus
本文提出并证明了一个拓扑递归关系，它用具有较少余切线类的不变量来表示具有至少一个余切线类的（3g-1）次幂的射影流形的任何亏格Gromov-Witten不变量.对于射影空间，我们证明了这些关系与Virasoro条件一起足以计算全Gromov-Witten势。这给出了确定射影空间的高亏格Gromov-Witten不变量的第一个计算上可行的方法。
Seiberg duality conjecture asserts that the Gromov-Witten theories (Gauged Linear Sigma Models) of two quiver varieties related by quiver mutations are equal via variable change. In this work, we prove this conjecture for $A_n$ type quiver varieties.
The product formula for Gromov-Witten invariants
证明了两个簇的乘积的Gromov-Witten不变量系等于两个因子的Gromov-Witten不变量系的张量积。
Given two equivariant vector bundles over an algebraic GKM manifold with the same equivariant Chern classes, we show that the genus zero equivariant Gromov--Witten theory of their projective bundles are naturally isomorphic.
Gromov-Witten invariants and rational curves on Grassmannians
研究了齐性空间X上s-点亏格零Gromov-Witten不变量的计数意义。为此，我们给出了X上的有理曲线的解释。
The degree of the variety of rational ruled surfaces and Gromov-Witten invariants
通过将问题与Gromov-Witten不变量和量子上同调相联系，计算了射影空间中d次有理直纹曲面的簇参数化次数.
Connected Gromov-Witten invariants of [Sym^n(A_r)]
本文研究了对称积栈[Sym^n（A_r）]的连通Gromov-Witten不变量理论。我们导出了所有具有两个插入的等变不变量的封闭形式表达式，并揭示了该理论与三重A_r x P^1的相对Gromov-Witten理论之间的自然对应。当n小于或等于3时，我们确定了[Sym^n（A_1）]的三点（通常）Gromov-Witten不变量.
We prove that the genus-0 invariants in K-theoretic Gromov--Witten theory are governed by an integrable hierarchy of hydrodynamic type. If the K-theoretic quantum product is semisimple, then we also prove the completeness of the hierarchy.
Given a smooth projective variety $X$ and a smooth divisor $D\subset X$. We study relative Gromov-Witten invariants of $(X,D)$ and the corresponding orbifold Gromov-Witten invariants of the $r$-th root stack $X_{D,r}$. For sufficiently large $r$, we prove that orbifold Gromov-Witten invariants of $X_{D,r}$ are polynomials in $r$. Moreover, higher genus relative Gromov-Witten invariants of $(X,D)$ are exactly the constant terms of the corresponding higher genus orbifold Gromov-Witten invariants of $X_{D,r}$. We also provide a new proof for the equality between genus zero relative and orbifold G…
Higher-genus Gromov-Witten invariants as genus 0 invariants of symmetric products
证明了一个表示投射簇X的后代亏格g Gromov-Witten不变量的公式，该公式表示投射簇X的对称积栈S^{g+1}（X）的亏格0不变量.当X为点时，后者为对称群的结构常数，从而获得了计算点的Gromov-Witten不变量的新方法。
Degeneration and gluing of Kuranishi structures in Gromov-Witten theory and the degeneration/gluing axioms for open Gromov-Witten invariants under a symplectic cut
本文研究了Gromov-Witten理论中Kuranishi结构在辛割下的退化和胶合。这导致我们的退化公理和粘合公理开放Gromov-Witten不变量。然后，它们提供了一条通过专业化构建虚拟基础链的途径。附录中给出了Li-Ruan/Li与Ionel-Parker关于封闭Gromov-Witten不变量的退化公式的等价性的评论。
A Uniqueness Theorem for Frobenius Manifolds and Gromov--Witten Theory for Orbifold Projective Lines
证明了对于至多有三个轨道点的轨道射影线，由Gromov-Witten理论构造的Frobenius结构是由具有一定自然初始条件的WDVV方程唯一确定的.
Invariance of Gromov--Witten theory under a simple flop
我们证明了Gromov-Witten不变量的母函数在扩展Kähler模空间中的解析延拓后，对于所有的属，在一个简单的触发器下是不变的。这是一个[LLL]的续集。
Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
证明了具有准素插入的非奇环面3重X的等变Gromov-Witten理论等价于X的等变Donaldson-Thomas理论。作为推论，Agangic，Klemm，Marino和Vafa的局部Calabi-Yau复曲面3-折叠的Gromov-Witten理论的拓扑顶点计算在全3-腿设置下被证明是正确的。
Invariance of tautological equations II: Gromov--Witten theory
第二部分的目的是探讨在Gromov-Witten理论领域重言式方程的不变性技术。主要结果是利用Gromov-Witten理论的技巧证明了不变性定理（文[14]中的不变性猜想~1）。建立了重言环的一般归纳结构，为重言环的研究提供了新的工具。
Degenerations of Del Pezzo surfaces and the Gromov-Witten invariants of the Hilbert Scheme of conics
利用退化方法研究了Del Pezzo曲面的示性数。
In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold $X$. We generalize the Givental formula which is studied in the smooth case in \cite{Giv2} \cite{Giv3} \cite{Giv4} to the orbifold case. Specifically, we recover the higher genus Gromov-Witten invariants of a GKM orbifold $X$ by its genus zero data. When $X$ is toric, the genus zero Gromov-Witten invariants of $X$ can be explicitly computed by the mirror theorem studied in \cite{CCIT} and our main theorem gives a closed formula for the all genus Gromov-Witten invariants of $X$. When $X$ is a toric Calabi-Yau 3-orbi…
Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations
我们考虑了相对Gromov-Witten理论和Gromov-Witten退化理论的四种方法：Jun Li的原始方法，Bumsig Kim的对数展开，Abramovich-Fantechi的orbifold展开，以及由于Gross-Siebert和Abramovich-Chen而没有展开的对数理论。我们展示了这些模空间的态射，并证明了他们的虚拟基本类是通过这些态射向前推进兼容。这意味着与所有四个理论相关的Gromov-Witten不变量是相同的。
The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of $V \times W$ with those of $V$ and $W$ in the case the log structure on $V$ is trivial.
Gromov-Witten theory of tame Deligne-Mumford stacks in mixed characteristic
定义了戴德金整环上有限表示的光滑真驯服Deligne-Mumford栈的Gromov-Witten类和不变量.我们证明了它们是形变不变量，并验证了基本公理。对于戴德金整环上光滑的真驯服Deligne-Mumford堆叠，证明了不同特征的纤维的不变量是相同的.证明了亏格为零的Gromov-Witten不变量定义了一个满足WDVV方程的势函数，并由此导出了亏格为零的Gromov-Witten不变量在任意特征下的重构定理.
We define the Gromov-Witten invariants for the parabolic bundles over an orbifold $C$ in various situation. Those bring us to refine this notion to get an accurate computation of the number of maximal subbundles of a sufficiently general parabolic bundle by means of the Intriligator-Varfa formula.
Computing Gromov-Witten invariants of some Fano varieties
对于具有一般驯服的半单量子（和小量子）（p，p）-型上同调的Fano簇，其第一Chern类是有效积分基因子的严格正组合，我们给出了一个从有限个初始不变量计算所有亏格为零的Gromov-Witten不变量的递归算法.
New recursions for genus-zero Gromov-Witten invariants
给出了复射影流形$X$的亏格为零的Gromov-Witten不变量之间的新关系.当$X$的上同调由除数类和“具有消失的一点不变量”的类生成时，这些关系根据一点不变量确定多点不变量。
We consider the question of how geometric structures of a Deligne-Mumford stack affect its Gromov-Witten invariants. The two geometric structures studied here are {\em gerbes} and {\em root constructions}. In both cases, we explain conjectures on Gromov-Witten theory for these stacks and survey some recent progress on these conjectures.
Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
我们构造了一般辛流形的Gromov-Witten不变量。
We prove that the Frobenius structure constructed from the Gromov-Witten theory for an orbifold projective line with at most $r$ orbifold points is uniquely determined by the WDVV equations with certain natural initial conditions.
A topological view of Gromov-Witten theory
我们通过退化和局部化相互作用提供的普适关系来研究相对的Gromov-Witten理论。我们发现相对Gromov-Witten理论完全由绝对Gromov-Witten理论决定。相对和绝对理论之间的关系是由一个强有力的类比经典拓扑指导。作为一个结果，我们提出了一个数学测定的Gromov-Witten不变量（在所有属）的Calabi-Yau五次3倍的已知理论。
We study the cycle-valued reduced Gromov-Witten theory of a nonsingular projective K3 surface. For primitive curve classes, we prove that the correspondence induced by the reduced virtual fundamental class respects the tautological rings. Our proof uses monodromy over the moduli space of K3 surfaces, degeneration formulae and virtual localization. As a consequence of the monodromy argument, we verify an invariance property for Gromov-Witten invariants of K3 surfaces in primitive curve class conjectured by Oberdieck-Pandharipande.
In this paper, we define genus-zero relative Gromov--Witten invariants with negative contact orders. Using this, we construct relative quantum cohomology rings and Givental formalism. A version of Virasoro constraints also follows from it.
We provide an enumerative meaning of the mirror maps for toric Calabi-Yau orbifolds in terms of relative Gromov-Witten invariants of the toric compactifications. As a consequence, we obtain an equality between relative Gromov-Witten invariants and open Gromov-Witten invariants. Therefore, the instanton corrected mirrors for toric Calabi-Yau orbifolds can be constructed using relative Gromov-Witten invariants.
Gromov-Witten invariants and quantum cohomology of Grassmannians
这是我在巴拿赫中心迷你学校的五个讲座的书面版本“舒伯特品种”，在华沙，2003年5月18日至22日。
Family Gromov-Witten Invariants for Kahler Surfaces
对于具有$p_g\geq 1$的Kähler曲面，通常的Gromov-Witten不变量为零。本文用解析方法定义了Kähler曲面的Gromov-Witten族不变量。我们证明，这些是定义良好的不变量的变形类的Kähler结构。
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。