Uniruledness of orthogonal modular varieties

Details Uniruledness of orthogonal modular varieties Uniruledness of orthogonal modular varieties

2012-02-15

arxiv.org/abs/1202.3361v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

A strongly reflective modular form with respect to an orthogonal group of signature (2,n) determines a Lorentzian Kac--Moody algebra. We find a new geometric application of such modular forms: we prove that if the weight is larger than n then the corresponding modular variety is uniruled. We also construct new reflective modular forms and thus provide new examples of uniruled moduli spaces of lattice polarised K3 surfaces. Finally we prove that the moduli space of Kummer surfaces associated to (1,21)-polarised abelian surfaces is uniruled.

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