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摘要翻译：
如果积分双曲格的自同构群是由直到有限指数的反射生成的，则称其为反射格。自1981年以来，人们知道它们的数量基本上是有限的。我们证明了具有反射Picard格的C上K3曲面可以用它们的自对应通过具有本原各向同性Mukai向量的束模的合成来刻画：它们在Picard格上的积分作用下的自对应在数值上等价于有限个特别简单的自对应通过束模的合成。这涉及两个主题:K3曲面通过轮模的自对应和算术双曲反射群。它还提出了几个自然未解决的相关问题。
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英文标题：
《Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic
hyperbolic reflection groups》
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作者：
Viacheslav V. Nikulin
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最新提交年份：
2009
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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：Mathematics 数学
二级分类：Geometric Topology 几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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英文摘要：
An integral hyperbolic lattice is called reflective if its automorphism group is generated by reflections, up to finite index. Since 1981, it is known that their number is essentially finite. We show that K3 surfaces over C with reflective Picard lattices can be characterized in terms of compositions of their self-correspondences via moduli of sheaves with primitive isotropic Mukai vector: Their self-correspondences with integral action on the Picard lattice are numerically equivalent to compositions of a finite number of especially simple self-correspondences via moduli of sheaves. This relates two topics: Self-correspondences of K3 surfaces via moduli of sheaves and Arithmetic hyperbolic reflection groups. It also raises several natural unsolved related problems.
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PDF链接：
https://arxiv.org/pdf/0810.2945
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