WonTae Hwang, Bo-Hae Im, Hansol Kim
We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.
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
Kawaguchi-Silverman conjecture on automorphisms of projective threefolds
本文将射影三维流形自同构的Kawaguchi-Silverman猜想归结为弱Calabi-Yau与有理连通两种情形，并证明非正则性满足q(X)≥dim X−1时猜想成立，同时探讨了Picard数为2的情形。
Let $k$ be a field of characteristic zero containing a primitive fifth root of unity. Let $X/k$ be a smooth cubic threefold with an automorphism of order five, then we observe that over a finite extension of the field actually the dihedral group $D_5$ is a subgroup of ${\rm Aut}(X)$. We find that the intermediate Jacobian $J(X)$ of $X$ is isogenous to the product of an elliptic curve $E$ and the self-product of an abelian surface $B$ with real multiplication by $\mathbb{Q}(\sqrt{5})$. We give explicit models of some algebraic curves related to the construction of $J(X)$ as a Prym variety. This…
Using the theory of polarised flag type quotients, we determine mass formulae for all principally polarised supersingular abelian threefolds defined over an algebraically closed field $k$ of characteristic $p$. We combine these results with computations of the automorphism groups to study Oort's conjecture; we prove that every generic three-dimensional principally polarised supersingular abelian variety over $k$ of characteristic $\neq 2$ has automorphism group $\{ \pm 1 \}$.
Iitaka fibrations and integral points: a family of arbitrarily polarized spherical threefolds
针对一族球面对数 Fano 三重 Fold 研究 Manin 纲领，确定任意丰富线丛高度有界整点的渐近数量，证实 Santens 猜想并推进饭高纤维化对数类比的理解。
Fano threefolds of genus 12 with large automorphism group in positive and mixed characteristic
本文研究了特征正和混合特征下 genus 12 的 Fano 三维簇具有大自同构群的情况，证明了其存在性条件及 Shafarevich 猜想的成立情况。
For each Sophie Germain prime $g \geq 5,$ we construct an absolutely simple polarized abelian variety of dimension $g$ over a finite field, whose automorphism group is a cyclic group of order $4g+2$. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.
We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.
We study birational transformations into elliptic fibrations and birational automorphisms of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces having terminal singularities classified by A.R. Iano-Fletcher, J. Johnson, J. Kollar, and M. Reid.
We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.
To any cubic surface, one can associate a cubic threefold given by a triple cover of $\mathbb P^3$ branched in this cubic surface. D. Allcock, J. Carlson, and D. Toledo used this construction to define the period map for cubic surfaces. It is interesting to calculate this map for some specific cubic surfaces. In this paper, we have calculated it in the case when the cubic surface is given by a triple covering of $\mathbb P^2$ branched in a smooth elliptic curve. In this case, the periods can be expressed through periods of the corresponding elliptic curve.
We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of simple polarized abelian fourfolds over finite fields. As an application, we compute the Jordan constants of the automorphism groups of simple abelian fourfolds over finite fields.
Jacobians with with automorphisms of prime order
本文针对容许素数阶p>2自同构的主极化阿贝尔簇开展研究，证明对自同构在第一类微分上作用的重数施加特定自然条件，可判定这类极化簇不是曲线的雅可比簇。
Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus Q_O of quaternionic multiplication by O in the moduli space A_g of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe Q_O as a union of Atkin-Lehner quotients of Shimura varieties and we compute the number of irreducible components of Q_O in terms of class numbers of CM-fields.
Let $\mathcal Q_D$ be the set of moduli points on Siegel's modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order $\mathcal O$ in an indefinite quaternion algebra of discriminant $D$ over $\mathbb Q$ such that the Rosati involution coincides with a positive involution of the form $α\mapstoμ^{-1}\overlineαμ$ on $\mathcal O$ for some $μ\in\mathcal O$ with $μ^2+D=0$. In this paper, we first give a formula for the number of irreducible components in $\mathcal Q_D$, strengthening an earlier result of Rotger. Then for each irr…
Let k be a field of characteristic different from 2. There can be an obstruction for an indecomposable principally polarized abelian threefold (A,a) over k to be a Jacobian over k. It can be computed in terms of the rationality of the square root of the value of a certain Siegel modular form. We show how to do this explicitly for principally polarized abelian threefolds which are the third power of an elliptic curve with complex multiplication. We use our numeric results to prove or refute the existence of some optimal curves of genus 3.
Automorphism groups of curves with simple Jacobians
研究特征为0的代数闭域上具有简单雅可比矩阵的光滑射影连通曲线的自同构群，通过构造曲线族并证明其密度为1的成员集有简单雅可比矩阵，在主极化阿贝尔簇模空间中给出无限多个新的不太可能的交的例子。
We prove that for any pair of integers 0\leq r\leq g such that g\geq 3 or r>0, there exists a (hyper)elliptic curve C over F_2 of genus g and 2-rank r whose automorphism group consists of only identity and the (hyper)elliptic involution. As an application, we prove the existence of principally polarized abelian varieties (A,λ) over F_2 of dimension g and 2-rank r such that \Aut(A,λ)={\pm 1}.
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。