Let X be a smooth complex projective variety, a: X → A a morphism to an abelian variety such that pic0(A) injects into pic0(X) and let L be a line bundle on X; denote by ha0(X,L) the minimum of h0(X,LS - a-α) for α Pic0(A). The so-called Clifford-Severi inequalities have been proven in [M. A. Barja, Generalized Clifford-Severi inequality and the volume of irregular varieties, Duke Math. J. 164(3) (2015) 541-568; M. A. Barja, R. Pardini and L. Stoppino, Linear systems on irregular varieties, J. Inst. Math. Jussieu (2019) 1-39; doi:10.1017/S1474748019000069]; in particular, for any L there is a lower bound for the volume given by: vol(L) ≥ n!ha0(X,L), and, if KX - L is pseudoeffective, vol(L) ≥ 2n!ha0(X,L). In this paper, we characterize varieties and line bundles for which the above Clifford-Severi inequalities are equalities.
Higher-dimensional Clifford-Severi equalities
Pardini R.;
2020-01-01
Abstract
Let X be a smooth complex projective variety, a: X → A a morphism to an abelian variety such that pic0(A) injects into pic0(X) and let L be a line bundle on X; denote by ha0(X,L) the minimum of h0(X,LS - a-α) for α Pic0(A). The so-called Clifford-Severi inequalities have been proven in [M. A. Barja, Generalized Clifford-Severi inequality and the volume of irregular varieties, Duke Math. J. 164(3) (2015) 541-568; M. A. Barja, R. Pardini and L. Stoppino, Linear systems on irregular varieties, J. Inst. Math. Jussieu (2019) 1-39; doi:10.1017/S1474748019000069]; in particular, for any L there is a lower bound for the volume given by: vol(L) ≥ n!ha0(X,L), and, if KX - L is pseudoeffective, vol(L) ≥ 2n!ha0(X,L). In this paper, we characterize varieties and line bundles for which the above Clifford-Severi inequalities are equalities.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.