Covers of algebraic varieties VI. Anglo--American covers and $(1,3)$--polarized abelian surfaces

Gianfranco Casnati

doi:10.4134/JKMS.2012.49.1.1

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2012; 49(1): 1-16

Printed January 1, 2012

https://doi.org/10.4134/JKMS.2012.49.1.1

Covers of algebraic varieties VI. Anglo--American covers and $(1,3)$--polarized abelian surfaces

Gianfranco Casnati

Politecnico di Torino

Abstract

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Abstract

In the present paper we describe a class of Gorenstein, finite and flat morphism $\varrho\colon X\to Y$ of degree $6$ of algebraic varieties, called Anglo--American covers. We prove a general Bertini theorem for them and we give some evidence that the cover $\varrho\colon A\to{\mathbb P}^2_k$ associated general $(1,3)$--polarized abelian surface is Anglo--American.

Keywords: cover of degree $d$, Anglo--American cover

MSC numbers: 14E20, 14E22