We use Galois closures of finite rational maps between complex projective varieties to introduce a new method for producing varieties such that the holomorphic part of the cup product map 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 greater than one.
Bastianelli, F., Pirola, G.p., 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;
2010-01-01
Abstract
We use Galois closures of finite rational maps between complex projective varieties to introduce a new method for producing varieties such that the holomorphic part of the cup product map 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 greater than one.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
