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 to rational contact curves in projective space with arbitrary incidence conditions are enumerative. Also, we use Bott formula on the Kontsevich space to find the exact value of those numbers.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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