Back to Algebraic Geometry Seminar: Fall 2011
Algebraic Geometry Seminar
Date: Tuesday, Sep 20, 2011
Time: 3:30PM - 4:30PM
Location: LCB 222
William D. Gillam
Brown University
Title |
Quotient schemes and stable pairs |
Abstract |
Let E be a rank two vector bundle over a Riemann surface C. The moduli space of stable pairs on E, in the sense of Pandharipande-Thomas, provides an alternative to the space of stable maps to E for the purpose of “counting” curves in the threefold E. The scaling action on E induces a torus action on the stable pairs moduli space. The moduli spaces of torus fixed stable pairs can be described as closed subschemes of products of quotient schemes of symmetric powers of E. The description is somewhat compatible with the obstruction theories. In favourable situations this can be used to express stable pairs invariants in terms of quotient scheme invariants—the latter being well-understood. In the “favourable situations” one thus obtains “explicit formulas” for the full descendant stable pairs theory of E. |
Algebraic Geometry