Instanton sheaves and components of the moduli space of semistable sheaves on the projective space.
Jardim, Marcos.
Instanton sheaves and components of the moduli space of semistable sheaves on the projective space. - Rio de Janeiro: IMPA, 2015. - video online
Talk.
Recent results by Tikhomirov, and by the author and Verbitsky have answered old questions about the geometry of the moduli space I(c) of rank 2 instanton bundles of charge c on the projective space: we now know that this is an irreducible, non-singular affine variety of dimension 8c-3. The next step is to study its compactification. Since every rank 2 instanton bundle on P^3 is stable, I(c) can be regarded as an open subset of the Gieseker--Maruyama scheme M(c) of semistable rank 2 torsion free sheaves on P^3 with Chern classes c_1=c_3=0 and c_2=c. One can then consider the closure of I(c) within M(c). In this talk we show that the singular locus of non-locally free rank 2 instanton sheaves on P^3 have pure dimension 1. We then describe certain irreducible components of the boundary of I(c) with dimension 8c-4. Such components consist of stable, non-locally free rank 2 instanton sheaves whose singular loci are rational curves. In addition, we describe new components of M(3) and M(5) consisting of stable, non-locally free rank 2 instanton sheaves whose singular loci are elliptic curves. The results presented are joint work with M. Gargate and with D. Markushevich and A. S. Tikhomirov .
Matematica.
Instanton sheaves and components of the moduli space of semistable sheaves on the projective space. - Rio de Janeiro: IMPA, 2015. - video online
Talk.
Recent results by Tikhomirov, and by the author and Verbitsky have answered old questions about the geometry of the moduli space I(c) of rank 2 instanton bundles of charge c on the projective space: we now know that this is an irreducible, non-singular affine variety of dimension 8c-3. The next step is to study its compactification. Since every rank 2 instanton bundle on P^3 is stable, I(c) can be regarded as an open subset of the Gieseker--Maruyama scheme M(c) of semistable rank 2 torsion free sheaves on P^3 with Chern classes c_1=c_3=0 and c_2=c. One can then consider the closure of I(c) within M(c). In this talk we show that the singular locus of non-locally free rank 2 instanton sheaves on P^3 have pure dimension 1. We then describe certain irreducible components of the boundary of I(c) with dimension 8c-4. Such components consist of stable, non-locally free rank 2 instanton sheaves whose singular loci are rational curves. In addition, we describe new components of M(3) and M(5) consisting of stable, non-locally free rank 2 instanton sheaves whose singular loci are elliptic curves. The results presented are joint work with M. Gargate and with D. Markushevich and A. S. Tikhomirov .
Matematica.