TY - JOUR

T1 - On deformations of curves supported on rigid divisors

AU - González-Alonso, Víctor

N1 - Funding information: The author developed this work with the support of the Spanish “Ministerio de Economía y Competitividad” (through the Project MTM2012-38122-C03-01/FEDER) and the “Generalitat de Catalunya” (through the Project 2009-SGR-1284). He was also partially supported by the Grant FPU-AP2008-01849 of the Spanish “Ministerio de Educación”, and by the ERC StG 279723 “Arithmetic of algebraic surfaces” (SURFARI).

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84956476922&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1401.7466

U2 - 10.1007/s10231-014-0455-x

DO - 10.1007/s10231-014-0455-x

M3 - Article

AN - SCOPUS:84956476922

VL - 195

SP - 111

EP - 132

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

SN - 0373-3114

IS - 1

ER -