Rational connectivity and sections of families over curves
Algebraic Geometry
2007-05-23 v1
Abstract
We show that if a family of complex varieties over a base B admits a section when restricted to a very general curve in B, then the family must contain a subfamily of rationally connected varieties dominating B. As an application, we deduce the existence of one parameter families of Enriques surfaces with no section.
Cite
@article{arxiv.math/0210225,
title = {Rational connectivity and sections of families over curves},
author = {T. Graber and J. Harris and B. Mazur and J. Starr},
journal= {arXiv preprint arXiv:math/0210225},
year = {2007}
}
Comments
21 pages