On deformations of curves supported on rigid divisors
arXiv:1401.7466
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).
Some typos corrected. Accepted for publication in the Annali di Matematica Pura ed Applicata