Seminars: A. S. Tikhomirov, New divisors in the boundary of the instanton moduli space

SEMINARS


Shafarevich Seminar January 27, 2015 17:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)

New divisors in the boundary of the instanton moduli space A. S. Tikhomirov
Abstract: This is a joint work with M. Jardim (Univ. Campinas) and D. Markushevich (Univ. Lille-1). We consider the moduli space $I(n)$ of rank $2$ instanton vector bundles of charge n on the projective space P3. It is known that $I(n)$ is an irreducible nonsingular affine variety of dimension $8n-3$. Since every rank $2$ instanton bundle on P3 is stable, one may regard $I(n)$ as an open subset of the projective Gieseker–Maruyama moduli scheme $M(n)$ of rank $2$ semistable torsion free sheaves on P3 with Chern classes $c_1=c_3=0$ and $c_2=n$, and consider the closure $II(n)$ of $I(n)$ in $M(n)$. We construct some of the irreducible components of dimension $8n-4$ of the boundary $II(n)\setminus I(n)$. These components generically lie in the smooth locus of $M(n)$ and consist of rank $2$ torsion free instanton sheaves with singularities along rational curves.