Let X be a complex projective variety and consider the morphism. We use Galois closures of finite rational maps to introduce a new method for producing varieties such that Ψk has non-trivial kernel. We then apply our result to the two-dimensional case and we construct a new family of surfaces which are Lagrangian in their Albanese variety. Moreover, we analyze these surfaces computing their Chern invariants, and proving that they are not fibred over curves of genus g≥2. The topological index of these surfaces is negative and this provides a counterexample to a conjecture on Lagrangian surfaces formulated in Barja et al. (2007) [3]. © 2010 Elsevier Inc.

Bastianelli, F., Pirola, G., Stoppino, L. (2010). Galois closure and Lagrangian varieties. ADVANCES IN MATHEMATICS, 225(6), 3463-3501 [10.1016/j.aim.2010.06.006].

Galois closure and Lagrangian varieties

BASTIANELLI, FRANCESCO
;
2010

Abstract

Let X be a complex projective variety and consider the morphism. We use Galois closures of finite rational maps to introduce a new method for producing varieties such that Ψk has non-trivial kernel. We then apply our result to the two-dimensional case and we construct a new family of surfaces which are Lagrangian in their Albanese variety. Moreover, we analyze these surfaces computing their Chern invariants, and proving that they are not fibred over curves of genus g≥2. The topological index of these surfaces is negative and this provides a counterexample to a conjecture on Lagrangian surfaces formulated in Barja et al. (2007) [3]. © 2010 Elsevier Inc.
Articolo in rivista - Articolo scientifico
Cup product map; Galois closure; Lagrangian surfaces;
English
2010
225
6
3463
3501
open
Bastianelli, F., Pirola, G., Stoppino, L. (2010). Galois closure and Lagrangian varieties. ADVANCES IN MATHEMATICS, 225(6), 3463-3501 [10.1016/j.aim.2010.06.006].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/21097
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