刚性超全纯层沿hyparkahler流形的扭量变形保持刚性
Rigid hyperholomorphic sheaves remain rigid along twistor deformations of the underlying hyparkahler manifold
摘要：
设S是K ~ 3曲面，M是S上稳定凝聚层的光滑射影2n维模空间.在M × M上存在秩为2n-2的自反超全纯层E_M，其在非对角点（F，G）上的纤维为Ext^1（F，G）.层E_M可以沿着某扭量路径变形为每个Kahler流形X变形等价于M的平方上的层E_X。证明了E_X是无穷小刚性的，并且Azumaya代数End（E_X）的同构类与扭量路径无关.这验证了arXiv：1310.5782和arXiv：1507.03108中关于K3曲面的非交换变形的假设，并使这两篇论文的结果成为无条件的。
英文摘要：
Let S be a K3 surface and M a smooth and projective 2n-dimensional moduli space of stable coherent sheaves on S. Over M x M there exists a rank 2n-2 reflexive hyperholomorphic sheaf E_M, whose fiber over a non-diagonal point (F,G) is Ext^1(F,G). The sheaf E_M can be deformed along some twistor path to a sheaf E_X over the cartesian square of every Kahler manifold X deformation equivalent to M. We prove that E_X is infinitesimally rigid, and the isomorphism class of the Azumaya algebra End(E_X) is independent of the twistor path chosen. This verifies conjectures in arXiv:1310.5782 and arXiv:1507.03108 on non-commutative deformations of K3 surfaces and renders the results of these two papers unconditional.
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