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Title:
Genus zero super Gromov Witten invariants via odd torus localization
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Abstract:
A major challenge in construction of supergeometric analogue of Gromov-Witten invariants is the suitable generalization of intersection theory. We propose to circumvent this difficulty by assuming a virtual torus localization theorem for the odd directions. That is, we construct a super virtual normal bundle to the torus-fixed loci of the moduli space of super stable maps, and compute the super Gromov-Witten invariants, via dividing by the equivariant Euler class of the super virtual normal bundle and intersecting with the virtual class of the torus fixed superstable maps. We define the super Gromov-Witten invariants of genus zero which satisfy generalized Kontsevich-Manin axioms. Furthermore, we present a recipe for calculation of super Gromov-Witten invariants of projective space. Based on joint work with Enno Keßler and Shing-Tung Yau.
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