Let (S,L) be a smooth, irreducible, projective, complex surface, polarized by a very ample line bundle L of degree d>35. In this paper we prove that K2S≥−d(d−6). The bound is sharp, and K2S=−d(d−6) if and only if d is even, the linear system |H0(S,L)| embeds S in a smooth rational normal scroll T⊂P5 of dimension 3, and here, as a divisor, S is linearly equivalent to d2Q, where Q is a quadric on T
Let (S, L) be a smooth, irreducible, projective, complex surface, polarized by a very ample line bundle L of degree d> 35. In this paper we prove that KS2≥-d(d-6). The bound is sharp, and KS2=-d(d-6) if and only if d is even, the linear system | H0(S, L) | embeds S in a smooth rational normal scroll T⊂ P5 of dimension 3, and here, as a divisor, S is linearly equivalent to d2Q, where Q is a quadric on T.
DI GENNARO, V., Franco, D. (2017). A lower bound for KS2. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 66(1), 69-81 [10.1007/s12215-016-0273-7].
A lower bound for KS2
Di Gennaro Vincenzo;
2017-01-01
Abstract
Let (S, L) be a smooth, irreducible, projective, complex surface, polarized by a very ample line bundle L of degree d> 35. In this paper we prove that KS2≥-d(d-6). The bound is sharp, and KS2=-d(d-6) if and only if d is even, the linear system | H0(S, L) | embeds S in a smooth rational normal scroll T⊂ P5 of dimension 3, and here, as a divisor, S is linearly equivalent to d2Q, where Q is a quadric on T.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.