The moduli component of the space of semistable rank-2 sheaves on ℙ3 with singularities of mixed dimension


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A new irreducible component of the Gieseker–Maruyama moduli scheme M(3) of semistable coherent sheaves of rank 2 with Chern classes c1 = 0, c2 = 3, and c3 = 0 on P3 such that its general point corresponds to a sheaf whose singular locus contains components of dimensions 0 and 1 is described. These sheaves are obtained by elementary transformations of stable reflexive sheaves of rank 2 with Chern classes c1 = 0, c2 = 2, and c3 = 2 along the projective line. The constructed family of sheaves is the first example of an irreducible component of a Gieseker–Maruyama scheme whose general point corresponds to a sheaf with singularities of mixed dimension.

作者简介

A. Ivanov

Higher School of Economics (National Research University)

编辑信件的主要联系方式.
Email: anivanov_1@edu.hse.ru
俄罗斯联邦, Moscow, 101000

A. Tikhomirov

Higher School of Economics (National Research University)

Email: anivanov_1@edu.hse.ru
俄罗斯联邦, Moscow, 101000

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