皮卡尔数 1 的法诺流形的切线束大和动力学刚度（附刘杰的附录）

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-08-12 DOI:10.1007/s00208-024-02955-0

Feng Shao, Guolei Zhong

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引用次数: 0

摘要

让 \(f:X\rightarrow Y\) 是皮卡尔数为 1 的法诺流形的一个投射态，它在一般点的 VMRT 不是对偶缺陷的。假设切线束 \(T_X\) 是大的。我们证明除非 \(Y\) 是投影空间，否则 \(f\) 是同构的。作为应用，我们探讨了完全相交、德尔佩佐流形和穆凯流形的切线束的大，以及它们的动力学刚度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu)

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Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu)

Let \(f:X\rightarrow Y\) be a surjective morphism of Fano manifolds of Picard number 1 whose VMRTs at a general point are not dual defective. Suppose that the tangent bundle \(T_X\) is big. We show that \(f\) is an isomorphism unless \(Y\) is a projective space. As applications, we explore the bigness of the tangent bundles of complete intersections, del Pezzo manifolds, and Mukai manifolds, as well as their dynamical rigidity.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.