论文标题
将Mukai的猜想推广到符号类别和Kostant游戏
Generalizing the Mukai Conjecture to the symplectic category and the Kostant game
论文作者
论文摘要
在本文中，我们提出了一个问题，即（广义）Mukai不平等是否存在紧凑的，正元单调的同成形歧管。我们首先提供了一种方法，使人们能够检查（广义）Mukai不平等现象。这仅利用歧管的几乎复杂结构以及所谓的广义希尔伯特多项式的零的分析，该结构考虑了所有可能的线束的Atiyah-Singer索引。我们将此方法应用于广义标志品种。为了找到相应的广义希尔伯特多项式的零，我们引入了Kostant游戏的修改版本，并研究其组合性能。
In this paper we pose the question of whether the (generalized) Mukai inequalities hold for compact, positive monotone symplectic manifolds. We first provide a method that enables one to check whether the (generalized) Mukai inequalities hold true. This only makes use of the almost complex structure of the manifold and the analysis of the zeros of the so-called generalized Hilbert polynomial, which takes into account the Atiyah-Singer indices of all possible line bundles. We apply this method to generalized flag varieties. In order to find the zeros of the corresponding generalized Hilbert polynomial we introduce a modified version of the Kostant game and study its combinatorial properties.
