Geometry of Rational Curves on Low degree Complete Intersections
arXiv:1310.3506
Abstract
For a smooth complete intersection X, we consider a general fiber \mathbb{F} of the evaluation map ev of Kontsevich moduli space \bar{M}_{0,m}(X,m)\rightarrow X^m and the forgetful functor F : \mathbb{F} \rightarrow \bar{M}_{0,m}. We prove that a general fiber of the map is a smooth complete intersection if is of low degree. The result sheds some light on the arithmetic and geometry of Fano complete intersections.
30 pages. The paper is significantly rewritten. More details are included in this version. The section of applications is shortened by omitting some results and proofs in the earlier version. (Submitted)