Volume 17, issue 2 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal Albanese dimension

Margarida Mendes Lopes, Rita Pardini and Gian Pietro Pirola

Geometry & Topology 17 (2013) 1205–1223

Given a smooth complex projective variety X, a line bundle L of X and v H1(OX), we say that v is k–transversal to L if the complex Hk1(L) Hk(L) Hk+1(L) is exact. We prove that if v is 1–transversal to L and s H0(L) satisfies s v = 0, then the first order deformation (sv,Lv) of the pair (s,L) in the direction v extends to an analytic deformation.

We apply this result to improve known results on the paracanonical system of a variety of maximal Albanese dimension, due to Beauville in the case of surfaces and to Lazarsfeld and Popa in higher dimension. In particular, we prove the inequality pg(X) χ(KX) + q(X) 1 for a variety X of maximal Albanese dimension without irregular fibrations of Albanese general type.

paracanonical system, irregular varieties, varieties of maximal Albanese dimension, numerical invariants
Mathematical Subject Classification 2010
Primary: 14C20, 14J29, 32G10
Received: 25 August 2012
Accepted: 31 January 2013
Published: 29 May 2013
Proposed: Richard Thomas
Seconded: Jim Bryan, Ronald Stern
Margarida Mendes Lopes
Centro de Análise Matemática, Geometria e Sistemas Dinâmicos
Departamento de Matemática
Instituto Superior Técnico
Universidade Técnica de Lisboa
Av. Rovisco Pais
1049-001 Lisboa, Portugal
Rita Pardini
Dipartimento di Matematica
Università di Pisa
Largo B. Pontecorvo 5
I-56127 Pisa, Italy
Gian Pietro Pirola
Dipartimento di Matematica
Università di Pavia
Via Ferrata 1
I-27100 Pavia, Italy