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