arXiv math/07026792007-02-23math.NTmath.AG

Moment Zeta Functions for Toric Calabi-Yau Hypersurfaces

Antonio Rojas-Leon, Daqing Wan

英文摘要：

We study in detail the family of Calabi-Yau hypersurfaces defined by x_1+...+x_n+1/(x_1...x_n)=t over a finite field k. We determine its local and global monodromy and the trivial factors of its moment zeta function and Dwork's unit root zeta function.

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。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

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

相关论文

Modularity of Calabi--Yau varieties: 2011 and beyond

This paper presents the current status on modularity of Calabi-Yau varieties since the last update in 2003. We will focus on Calabi-Yau varieties of dimension at most three. Here modularity refers to at least two different types: arithmetic modularity and geometric modularity. These will include: (1) the modularity (automorphy) of Galois representations of Calabi-Yau varieties (or motives) defined over Q or number fields, (2) the modularity of solutions of Picard--Fuchs differential equations of families of Calabi-Yau varieties, and mirror maps (mirror moonshine), (3) the modularity of generat…

2012-12-18math.AGmath.NT

Construction and examples of higher-dimensional modular Calabi-Yau manifolds

We construct several examples of higher-dimensional Calabi-Yau manifolds and prove their modularity.

2006-02-02math.AGmath.NT

Zeta-functions of certain K3 fibered Calabi--Yau threefolds

We consider certain $K3$-fibered Calabi--Yau threefolds. One class of such Calabi--Yau threefolds are constructed by Hunt and Schimmrigk using twist maps. They are realized in weighted projective spaces as orbifolds of hypersurfaces. Our main goal of this paper is to investigate arithmetic properties of these Calabi--Yau threefolds. We also consider deformations of our Calabi--Yau threefolds, and we study the variation of the zeta-functions using $p$-adic rigid cohomology theory.

2009-11-04math.AGmath.NT

Small Resolutions and Non-Liftable Calabi-Yau threefolds

We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau threefolds. In particular, we construct a smooth projective Calabi-Yau threefold over $\F_3$ that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over $\F_5$ having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over $\F_p$ that do not lift to algebraic spaces in characteristic zero.

2008-04-09math.AGmath.NT

Automorphy of Calabi-Yau threefolds of Borcea-Voisin type over Q

We consider Calabi-Yau threefolds of Borcea-Voisin type over Q. They are constructed from products of K3 surfaces and elliptic curves. We use concrete K3 surfaces and discuss the automorphy of the Galois representations associated to the Calabi-Yau threefolds. The moduli spaces of these Calabi-Yau threefolds are Shimura varieties. Our result shows the existence of a CM point in the moduli space. We also consider mirror symmetry of Calabi-Yau threefolds.

2014-04-05math.AGmath.NT

Update on Modular Non-Rigid Calabi-Yau Threefolds

We review some recent results on the modularity of non-rigid Calabi-Yau threefolds.

2008-02-29math.AGmath.NT

更多相关论文收起更多论文

Non-liftable Calabi-Yau spaces

We construct many new non-liftable three-dimensional Calabi-Yau spaces in positive characteristic. The technique relies on lifting a nodal model to a smooth rigid Calabi-Yau space over some number field as introduced by the first author and D. van Straten.

2010-08-12math.AGmath.NT

Abelian Calabi-Yau threefolds: Néron models and rational points

We study Calabi-Yau threefolds fibered by abelian surfaces, in particular, their arithmetic properties, e.g., Néron models and Zariski density.

2016-10-08math.AGmath.NT

On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces

We prove that (not necessarily rigid) Calabi-Yau threefolds defined over the rationals which contain sufficiently many elliptic ruled surfcaes are modular (under mild restrictions on the primes of bad reduction). Our proof uses the results of Dieulefait and Manoharmayum who proved modularity of rigid Calabi-Yau threefolds.

2005-02-08math.AGmath.NT

普通卡拉比-丘三维簇的塔特猜想

The Tate Conjecture for Ordinary Calabi-Yau Threefolds

Oxford University（牛津大学）；CNRS (Université Paris–Saclay)（法国国家科学研究中心（巴黎-萨克雷大学））

该研究利用典范提升理论，证明有限域上普通卡拉比-丘三维簇的积分几何塔特猜想及部分普通卡拉比-丘簇除子类的对应猜想。

2026-10-12math.AGmath.NT

高度对称的Calabi-Yau Grassmannian超曲面的形变

Deformations of highly symmetric Calabi-Yau Grassmannian hypersurfaces

本文运用算术与Hodge理论技术研究Grassmannians及其商空间中高度对称超曲面实现的Calabi-Yau簇的铅笔，证明其几何性质不同于经典镜像。

2024-03-23math.AGmath.NT

Some Siegel threefolds with a Calabi-Yau model

In the following we describe some examples of Calabi-Yau manifolds, which arise as desingularizations of certain Siegel threefolds. The first Siegel modular variety with a Calabi-Yau model and the essentially only one up to now has been discovered by Barth and Nieto.

2009-11-27math.AGmath.NT

The modularity conjecture for rigid Calabi-Yau threefolds over Q

We formulate the modularity conjecture for rigid Calabi-Yau threefolds defined over the field Q of rational numbers. We establish the modularity for the rigid Calabi-Yau threefold arising from the root lattice A_3. Our proof is based on geometric analysis.

2000-09-18math.AGmath.NT

Modularity of rigid Calabi-Yau threefolds over Q

We prove modularity for a huge class of rigid Calabi-Yau threefolds over $\Q$. In particular we prove that every rigid Calabi-Yau threefold with good reduction at 3 and 7 is modular.

2003-04-29math.NT

Calabi-Yau 变种的 Hasse-Witt 不变量

Hasse-Witt invariants of Calabi-Yau varieties

本文通过Cartier算子和Calabi-Yau模形式理论定义Calabi-Yau变种的Hasse-Witt不变量，并提出两者等价的猜想，提供了多个例子支持该猜想。

2026-05-14math-phmath.AGmath.MP