Please use this identifier to cite or link to this item:
Title: On the Xiao conjecture for plane curves
Author: Favale, F.
Naranjo del Val, Juan Carlos
Pirola, G. P.
Keywords: Corbes planes
Plane curves
Issue Date: Aug-2018
Publisher: Springer Verlag
Abstract: Let f:S⟶B be a non-trivial fibration from a complex projective smooth surface S to a smooth curve B of genus b. Let cf the Clifford index of the general fibre F of f. In Barja et al. (Journal für die reine und angewandte Mathematik, 2016) it is proved that the relative irregularity of f, qf=h1,0(S)−b is less or equal than or equal to g(F)−cf . In particular this proves the (modified) Xiao's conjecture: qf≤g(F)2+1 for fibrations of general Clifford index. In this short note we assume that the general fiber of f is a plane curve of degree d≥5 and we prove that qf≤g(F)−cf−1 . In particular we obtain the conjecture for families of quintic plane curves. This theorem is implied for the following result on infinitesimal deformations: let F a smooth plane curve of degree d≥5 and let ξ be an infinitesimal deformation of F preserving the planarity of the curve. Then the rank of the cup-product map H0(F,ωF)⟶⋅ξH1(F,OF) is at least d−3 . We also show that this bound is sharp.
Note: Versió postprint del document publicat a:
It is part of: Geometriae Dedicata, 2018, vol. 195, num. 1, p. 193-201
Related resource:
ISSN: 0046-5755
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

Files in This Item:
File Description SizeFormat 
673276.pdf153.3 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.