Maps from K-trivial varieties and connectedness problems
Annales Henri Lebesgue, Volume 3 (2020) , pp. 473-500.

Metadata

KeywordsCalabi–Yau varieties, families of elliptic curves, elliptically (chain) connected varieties

Abstract

In this paper we study varieties covered by rational or elliptic curves. First, we show that images of Calabi–Yau or irreducible symplectic varieties under rational maps are almost always rationally connected. Second, we investigate elliptically connected and elliptically chain connected varieties, and varieties swept out by a family of elliptic curves. Among other things, we show that Calabi–Yau or hyperkähler manifolds which are covered by a family of elliptic curves contain uniruled divisors and that elliptically chain connected varieties of dimension at least 2 contain a rational curve, and so do K-trivial varieties with finite fundamental group which are covered by elliptic curves.


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