Year: 2020
Type: article
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.
Source: Annales Henri Lebesgue
DOI: 10.5802/ahl.38
Authors: Vladimir Lazić, Thomas Peternell
Institutions: Saarland University, University of Bayreuth
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2886034650