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arXiv · 1401.7466

On deformations of curves supported on rigid divisors

Víctor González-Alonso
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Abstract

Motivated by a conjecture of Xiao, we study supporting divisors of fibred surfaces. On the one hand, after developing a formalism to treat one-dimensional families of varieties of any dimension, we give a structure theorem for fibred surfaces supported on relatively rigid divisors. On the other hand, we study how to produce supporting divisors by constructing a global adjoint map for a fibration over a curve (generalizing the infinitesimal constructions of Collino, Pirola, Rizzi and Zucconi).

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Víctor González-Alonso. 2014-09-29. On deformations of curves supported on rigid divisors. https://arxiv.org/abs/1401.7466

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