How to compute enumerative invariants from residues?
A Special Lecture by Taro Kimura
Many examples of enumerative invariants appearing in the context of algebraic geometry are given by integrating over the moduli space of maps, sheaves, and so on. When there exists a nice group action on it, we may compute such invariants based on the fixed point contributions, i.e., the equivariant localization formula. In this talk, I'd like to explain an alternative use of the localization formula based on the Jeffrey-Kirwan residue formula for multi-variable contour integrals. The key idea is to use the residue of the poles appearing in the integral to classify and evaluate the fixed point contribution under the equivariant action. I'll demonstrate this formalism with several examples, including the equivariant DT/PT invariants for the affine spaces C^3 and C^4.
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- Room 7.07, Hans Freudenthaal Building