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 Hk−1(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.

Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal albanese dimension

PARDINI, RITA;
2013

Abstract

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 Hk−1(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.
Mendes Lopes, M.; Pardini, Rita; Pirola, G. P.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/233328
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