Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions

Details Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions

2006-06-18

arxiv.org/abs/math/0606429v1

Mathematics

Symplectic Geometry

79 pages

Scientific paper

We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, the new invariants coincide with Welschinger's invariant counts of real pseudoholomorphic curves. Furthermore, we calculate the new invariant for the real quintic threefold in genus 0 and degree 1 to be 30.

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