On the Space of Conics on Complete Intersections

Abstract

We get sharp degree bound for generic smoothness and connectedness of the space of conics in low degree complete intersections which generalizes the old work about Fano scheme of lines on Hypersurfaces.

8 pages, minor typos are corrected, some reference are added and a new application about the triviality of 1-Griffiths group of Fano complete intersections with index $\ge 2$ is included