Algebraic Geometry and Topological Strings Seminar 

10/11/2005, 15:00 — 16:00 — Amphitheatre Pa3, Mathematics Building
Tom Graber, University of California, Berkeley

Quantum Cohomology of Orbifolds and their Crepant Resolutions

I will discuss joint work with Jim Bryan in which we show how to modify the definition of the small quantum cohomology of an orbifold to take into account divisorial twisted sectors. This quantum cohomology is conjecturally very closely related to the quantum cohomology of any crepant resolution of singularities. In particular, we can directly verify this conjecture in a strong form in the example where the orbifold is the n'th symmetric product of the complex plane, with crepant resolution given by the Hilbert scheme of points.

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REFERENCES:

J. Bryan, R. Pandharipande, The local Gromov-Witten theory of curves, math.AG/0411037.
A. Okounkov, R. Pandharipande, The quantum cohomology of the Hilbert scheme of points in the plane, math.AG/0411210.