# Geometry of moduli space of rational curves on complete intersections

## Xuanyu Pan (Columbia)

For a low degree smooth complete intersection X, we consider the general fiber F of the following evaluation map ev of Kontsevich moduli space. $$ev: \overline{M}_{0,m}(X,m) \rightarrow X^m.$$ I will give general structure theorems of F. It answers questions relating to (1) Rational connectedness of moduli space (2) Enumerative geometry (3) The Search for a new 2-Fano variety (4) Picard group of moduli space.

Tuesday, January 8th, at 4:00pm in HBH 227