Abstract: Given a 2n-dimensional smooth complex variety equipped with a non-degenerate holomorphic 2-form, an n-dimensional subvariety is called Lagrangian if the form vanishes identically on it. Lagrangian varieties often provide interesting counterexamples and give rise to subtle geometric phenomena. One way to construct such varieties is by considering the Galois closure of a rational map between smooth varieties, which can be embedded in its Albanese variety as a Lagrangian subvariety. In this talk, we will discuss some geometric properties of a class of surfaces obtained in this way.
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