2017/03/31 by A. N. Ivanov, Alexey N. Ivanov, Alexander S. Tikhomirov +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Character (mathematics) #Coherent sheaf #Combinatorics #Dimension (graph theory) #Discrete mathematics #Disjoint sets #Geometry #Gravitational singularity #Mathematical analysis #Mathematics #Moduli space #Pure mathematics #Rank (graph theory) #Scheme (mathematics) #Zero (linguistics) #math.AG
paper · pdf · doi:10.1016/j.geomphys.2018.02.018
16 pages, 1 table
openalex created_date 2017/03/23 · arxiv created 2017/08/03 · openalex publication_date 2018/03/05 · arxiv updated 2018/04/18 · openalex updated_date 2026/08/05
We describe new irreducible components of the Gieseker-Maruyama moduli scheme M(3) of semistable rank 2 coherent sheaves with Chern classes c1=0, c2=3, c3=0 on ℙ3, general points of which correspond to sheaves whose singular loci contain components of dimensions both 0 and 1. These sheaves are produced by elementary transformations of stable reflexive rank 2 sheaves with c1=0, c2=2, c3=2 or 4 along a disjoint union of a projective line and a collection of points in ℙ3. The constructed families of sheaves provide first examples of irreducible components of the Gieseker-Maruyama moduli scheme such that their general sheaves have singularities of mixed dimension.