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

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 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
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - Geometria
English
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.
Castelnuovo–Halphen’s theory; Projective surface; Rational normal scroll;
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].
DI GENNARO, V; Franco, D
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/198047
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