Rationally cubic connected manifolds I: manifolds covered by lines
Algebraic Geometry
2010-03-26 v1
Abstract
In this paper we study smooth complex projective polarized varieties (X,H) of dimension n \ge 2 which admit a dominating family V of rational curves of H-degree 3, such that two general points of X may be joined by a curve parametrized by V, and such that there is a covering family of rational curves of H-degree one. Our main result is that the Picard number of these manifolds is at most three, and that, if equality holds, (X,H) has an adjuction theoretic scroll structure over a smooth variety.
Keywords
Cite
@article{arxiv.1003.4936,
title = {Rationally cubic connected manifolds I: manifolds covered by lines},
author = {Gianluca Occhetta and Valentina Paterno},
journal= {arXiv preprint arXiv:1003.4936},
year = {2010}
}