Studies on Hodge Theory and Hypergeometric Functions

霍奇理论与超几何函数研究

• 批准号: 09640010
• 负责人: KAWAMATA Yujiro
• 金额: $ 1.41万
• 依托单位: THE UNIVERASITY OF TOKYO
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640010/
• 关键词: alsebraic variety; pluricanonical form; Kodaira dimension; logarithmic form; multiplier ideal; canonical singularity; deformation; plurigenus; ホッジ理論; 標準因子; 半正値性; 消滅定理; 藤田予想; カラビ・ヤウ多様体

In the course of the investigation of the structure of algebraic varieties, it is often very helpful to look at the pluricanonical forms on the given varieties. For example, the Kodaira dimension of a variety is the order of growth of the m-genus, the dimension of the vector space of m-canonical forms, as a function on the integer m. This is a fundamental invariant for the birational classification of algebraic varieties. We investigated the problem of comparing log pluricanonical forms on a given variety with pluricanonical forms on its subvariety.Let X be a smooth algebraic variety and Y a smooth divisor. For example, Y is a compact algebraic manifold and X is the total space of its deformation family. We considered the problem of extending pluricanonical forms on Y to log pluricanonical forms on X.We defined sequences of multiplier ideal sheaves on X and Y, and the extension problem is reduced to the problem of the inclusion relationships among these ideals. We proved an extension theorem under some conditions. As applications. we proved that any deformations of canonical singularities are canonical, and that the plurigenus is constant on any deformation family of varieties of general type with only canonical singularities.

在研究代数品种结构的过程中，查看给定品种上的多元形式通常非常有帮助。例如，多样性的Kodaira维度是M-Genus的生长顺序，M-Canonical形式的向量空间的维度，作为整数m的函数。这是代数品种的寓言分类的基本不变。我们调查了在给定品种上比较对数多元形式的问题的问题，其子变量上的多个形式。letx是平滑的代数品种，y是平滑的除数。例如，Y是一个紧凑的代数歧管，X是其变形家族的总空间。我们考虑了将Y上的多元形式扩展到X上的多元形式的问题。我们确定了x和y上乘数理想束的序列，扩展问题降低到这些理想之间包含关系的问题。在某些条件下，我们证明了扩展定理。作为应用。我们证明了规范奇点的任何变形都是规范的，并且plurigenus在任何只有规范奇点的通用类型的变形族上都是恒定的。

项目成果

川又雄二郎: "On the cone of divisors of Calabi-Yanfiberspuces" Internat.J.Math.8. 665-687 (1997)

Yujiro Kawamata：“关于 Calabi-Yan Fiberspuces 的约数锥体”Internat.J.Math.8 (1997)。

川又雄二郎: "On the cone of divisors of Calabi-Yan fiber space" Internat.J.Math.8. 665-687 (1997)

Yujiro Kawamata：“关于 Calabi-Yan 纤维空间的约数锥体”Internat.J.Math.8 (1997)。

川又雄二郎: "On the cone of Calabi-Yau fiber spaces" Internat.J.Math. 8. 665-687 (1997)

Yujiro Kawamata：“关于 Calabi-Yau 纤维空间的锥体”Internat.J.Math。8. 665-687 (1997)

川又雄二郎: "On Fujifa's freeness conjecfure for 3-folds and 4-folds" Math.Annasen. 308. 419-505 (1997)

Yujiro Kawamata：“论 Fujifa 的 3 倍和 4 倍自由猜想”Math.Annasen 308. 419-505 (1997)

川又雄二郎: "代数多様体論" 共立出版, 223 (1997)

Yujiro Kawamata：《代数簇论》Kyoritsu Shuppan，223（1997）