A concrete approach to virtual classes in genus 0 Gromov--Witten theory

Abstract: Gromov--Witten theory is concerned with counting curves inside (smooth) projective varieties satisfying some incidence conditions (e.g. how many rational degree d curves pass through 3d-1 generic points in the complex projective plane?). In general (due to complications arising from the fact that spaces of curves may not be smooth), instead of counting curves directly, we need to use intersection theory on the space of curves to define certain "virtual counts". In the first half of the talk, we will provide the necessary background (spaces of curves, "expected dimension", compactness and some examples of curve counting). In the second half of the talk, we will describe a concrete differential geometric approach to these "virtual counts" for genus 0 curves in projective varieties (using ideas coming from the theory of psuedo-holomorphic curves in symplectic manifolds).

algebraic geometryalgebraic topologydifferential geometry

Audience: researchers in the topic

CMI seminar series

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