Rational connectivity and sections of families over curves

Details Rational connectivity and sections of families over curves Rational connectivity and sections of families over curves

2002-10-15

arxiv.org/abs/math/0210225v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

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.

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