Enumeration of rational contact curves via torus actions

Abstract: Complex projective spaces of odd dimension have a unique contact structure. So, in these spaces we have contact (Legendrian) rational curves. We are interested in enumeration of such curves. We prove that some Gromov-Witten numbers associated with rational contact curves in projective space with arbitrary incidence conditions are enumerative. Also, we use the Bott formula on the Kontsevich space to find the exact value of those numbers.

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon