Local Gromov-Witten Invariants of Spin Curves

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Junho Lee, University of Central Florida
Fine Hall 314

This is a joint work with Thomas H. Parker. We define a new type of symplectic “local Gromov-Witten invariant” of spin curves. When $X$ is a Kahler surface with a smooth canonical divisor $D$, its (full) GW invariants are expressed in terms of such local invariants, which in turn are universal functions determined by the normal bundle of the canonical divisor $D$. We also show that how these local GW invariants arise from an obstruction bundle (in the sense of Taubes) over the space of stable maps into curves. This yields an interesting theorem relating two- and four-dimensional Gromov-Witten theory. We also explicitly compute these local invariants in some cases.