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Regular version of the site

Article

The Moduli Component of the Space of Semistable Rank-2 Sheaves on P3 with Singularities of Mixed Dimension

Doklady Mathematics. 2017. Vol. 96. No. 2. P. 506-509.

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 classesc1=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.