| Título: | Normal presentation on elliptic ruled surfaces. |
| Autores: | Gallego Rodrigo, Francisco Javier ; Purnaprajna, Bangere P. |
| Tipo de documento: | texto impreso |
| Editorial: | Academic Press, 1996 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/restrictedAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometria algebraica , Tipo = Artículo |
| Resumen: |
From the introduction: Let X be an irreducible projective variety and L a very ample lLine bundle on X, whose complete linear series defines 'L : X ! P(H0(L)). Let S = 1 m=0 SmH0(X,L) and let R(L) = L1 n=0 H0(X,L n) be the homogeneous coordinate ring associated to L. Then R is a finitely generated graded module over S, so it has a minimal graded free resolution. We say that the line bundle L is normally generated if the natural maps SmH0(X,L) ! H0(X,L m) are surjective for all m 2. If L is normally generated, then we say that L satisfies property Np, if the matrices in the free resolution of R over S have linear entries until the p-th stage. In particular, property N1 says that the homogeneous ideal I of X in P(H0(L)) is generated by quadrics. A line bundle satisfying property N1 is also called normally presented. Let R = kR1R2. . . be a graded algebra over a field k. The algebra R is a Koszul ring iff TorRi (k, k) has pure degree i for all i. In this article we determine exactly (theorem 4.2) which line bundles on an elliptic ruled surface X are normally presented. As a corollary we show that Mukai’s conjecture is true for the normal presentation of the adjoint linear series for an elliptic ruled surface. In section 5 of this article, we show that if L is normally presented on X then the homogeneous coordinate ring associated to L is Koszul. We also give a new proof of the following result due to Butler: If deg(L) 2g + 2 on a curve X of genus g, then L embeds X with Koszul homogeneous coordinate ring. |
| En línea: | https://eprints.ucm.es/id/eprint/15418/1/15.pdf |
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