点的Hilbert格式上的大和Nef同义向量束

IF 0.9 3区 物理与天体物理 Q2 MATHEMATICS
D. Oprea
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引用次数: 3

摘要

我们研究了曲面上点的Hilbert格式上的重言向量丛。对于每个K-平凡曲面,我们写下一个简单的准则,确保重言丛是大的和nef的,并通过例子加以说明。在K3情况下,我们将Bini、Boissi和Flamini最近的构造和结果从2和3点的Hilbert格式扩展到任意数量的点。在K平凡曲面中,Enriques曲面的情况是最复杂的。我们的技术适用于其他光滑投影曲面,包括K3s的放大和一般类型的极小曲面,以及曲线的准时Quot格式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points
We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each K-trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the K3 case, we extend recent constructions and results of Bini, Boissi\`ere and Flamini from the Hilbert scheme of 2 and 3 points to an arbitrary number of points. Among the K-trivial surfaces, the case of Enriques surfaces is the most involved. Our techniques apply to other smooth projective surfaces, including blowups of K3s and minimal surfaces of general type, as well as to the punctual Quot schemes of curves.
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
87
审稿时长
4-8 weeks
期刊介绍: Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.
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