A long-standing problem in Algebraic Geometry and Commutative Algebra is to determine the minimal graded free resolution of a 0- dimensional scheme Z in Pn or in an arbitrary projective variety X. In [18], M. Musta ¸ta (1998) predicted the graded Betti numbers of ˘ the minimal free resolution of a general set of distinct points Z in X. In this paper, we state a refined version of Musta ¸ta’s con- ˘ jecture (MRC) and we predict the existence of a non-empty open subset U ⊂ Hilbs (X) such that any [Z] ∈ U has a minimal graded free resolution without ghost terms (WMRC). In this paper, we are going to prove: (1) for any s d+3 3 − 1 there exists a d+2 2 - dimensional family of irreducible generically smooth surfaces of degree d in P3 satisfying the WMRC for s; and (2) any smooth cubic surface satisfies the MRC for any s 19
Minimal free resolution for points on surfaces / Miró-Roig, Rosa M.; Pons-Llopis, Juan Francisco. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 357(2012), pp. 304-318. [10.1016/j.jalgebra.2012.01.034]
Titolo: | Minimal free resolution for points on surfaces | |
Autori: | ||
Data di pubblicazione: | 2012 | |
Rivista: | ||
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jalgebra.2012.01.034 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
1-s2.0-S0021869312000919-main.pdf | articolo principale | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2859414