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INICIO |
27 de julio de 2024
Faisceaux cohérents sur les courbes multiples.
| Título original | Faisceaux cohérents sur les courbes multiples. |
|---|---|
| Título inglés | Coherent sheaves on multiple curves. |
| Título español | Haces coherentes sobre curvas múltiples. |
| Autor/es | Drézet, Jean-Marc |
| Organización | Inst. Math. Jussieu, París, Francia |
| Revista | 0010-0757 |
| Publicación | 2006, 57 (2): 121-171, 36 Ref. |
| Tipo de documento | articulo |
| Idioma | Francés |
| Resumen inglés | This paper is devoted to the study of coherent sheaves on non reduced curves that can be locally embedded in smooth surfaces. If Y is such a curve then there is a filtration C Ì C2 Ì ... Ì Cn = Y such that C is the reduced curve associated to Y, and for very P Î C there exists z Î OY,P such that (zi) is the ideal of Ci in OY,P. We define, using canonical filtrations, new invariants of coherent sheaves on Y: the generalized rank and degree, and use them to state a Riemann-Roch theorem for sheaves on Y. We define quasi locally free sheaves, which are locally isomorphic to direct sums of OCi, and prove that every coherent sheaf on Y is quasi locally free on some nonempty open subset of Y. We give also a simple criterion of quasi locally freeness. We study the ideal sheaves In,Z in Y of finite subschemes Z of C. When Y is embedded in a smooth surface we deduce some results on deformations of In,Z (as sheaves on S). When n = 2, i.e. when Y is a double curve, we can completely describe the torsion free sheaves on Y. In particular we show that these sheaves are reflexive. The torsion free sheaves of generalized rank 2 on C2 are of the form I2,Z Ä L, where Z is a finite subscheme of C and L is a line bundle on Y. We begin the study of moduli spaces of stable sheaves on a double curve, of generalized rank 3 and generalized degree d. These moduli spaces have many components. Sometimes one of them is a multiple structure on the moduli space of stable vector bundles on C of rank 3 and degree d. |
| Clasificación UNESCO | 120101 |
| Palabras clave español | Curvas algebraicas ; Espacio de moduli ; Haces vectoriales |
| Código MathReviews | MR2223850 |
| Código Z-Math | Zbl 1106.14019 |
 Acceso al artículo completo |
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