[数学] 爆炸时的反常相干滑轮。II.翻墙和贝蒂 数字公式 [推广有奖]

摘要翻译：
这是研究射影曲面在点上爆破时一类相干束的模空间的系列论文的第二篇。我们称之为稳定逆相干束。本文的主要结果如下：a）我们描述了与例外因子相关的线丛的扭曲引起的模空间间的穿墙现象。b）给出了稳定反向相干束模空间的虚Hodge数的计算公式。此外，我们还证明了我们在ARXIV:0802.3120:c中的一个特例中观察到的结果。当第一Chern类与例外因子正交时，稳定反向相干束的模空间与原曲面上通常的稳定相干束的模空间同构。d）通过与异常曲线相关的线束的足够大的负幂，扭转后的模空间与爆破上稳定相干滑轮的通常模空间同构，因此爆破上稳定滑轮的通常模空间与原始曲面通过壁面交叉连接。
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英文标题：
《Perverse coherent sheaves on blow-up. II. wall-crossing and Betti
  numbers formula》
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作者：
Hiraku Nakajima and Kota Yoshioka
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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英文摘要：
  This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up of a projective surface at a point. The followings are main results of this paper: a) We describe the wall-crossing between moduli spaces caused by twisting of the line bundle associated with the exceptional divisor. b) We give the formula for virtual Hodge numbers of moduli spaces of stable perverse coherent sheaves.   Moreover we also give proofs of the followings which we observed in a special case in arXiv:0802.3120: c) The moduli space of stable perverse coherent sheaves is isomorphic to the usual moduli space of stable coherent sheaves on the original surface if the first Chern class is orthogonal to the exceptional divisor. d) The moduli space becomes isomorphic to the usual moduli space of stable coherent sheaves on the blow-up after twisting by sufficiently large negative power of the line bundle associated with the exceptional curve.   Therefore usual moduli spaces of stable sheaves on the blow-up and the original surfaces are connected via wall-crossings.
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PDF链接：
https://arxiv.org/pdf/0806.0463