Higher-Genus Gromov-Witten Invariants and Crepant Resolutions

4 November 2008
Let X be a Gorenstein orbifold and Y a crepant resolution of X. Suppose that the quantum cohomology algebra of Y is semisimple. We describe joint work with Iritani which shows that in this situation the genus-zero crepant resolution conjecture implies a higher-genus version of the crepant resolution conjecture. We expect that the higher-genus version in fact holds without the semisimplicity hypothesis.
  • Algebraic and Symplectic Geometry Seminar