Smoothness of the moduli space of complexes of coherent sheaves on an abelian or a projective K3 surface

2010/02/02 by Michi-aki Inaba, Inaba, Michi-aki
Mathematics · #14D20 #18E30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1002.0379

openalex publication_date 2010/02/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

For an abelian or a projective K3 surface X over an algebraically closed field k, consider the moduli space \splcpx_X/k\uet of the objects E in D^b(Coh(X)) satisfying \Ext^-1_X(E,E)=0 and \Hom(E,E)≅ k. Then we can prove that \splcpx_X/k\uet is smooth and has a symplectic structure.

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