The rank of the multiplication map for sections of bundles on curves

Ballico, E.

Ballico, E.

Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 677-683 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

Sia $X$ una curva liscia di genere $g \geq 2$ ed $A$ , $B$ fasci coerenti su $X$ . Sia $μ_{A, B} : H^{0} (X, A) \otimes H^{0} (X, B) \to H^{0} (X, A \otimes B)$ l'applicazione di moltiplicazione. Qui si dimostra che $μ_{A, B}$ ha rango massimo se $A ≅ ω_{X}$ e $B$ è un fibrato stabile generico su $X$ . Diamo un'interpretazione geometrica dell'eventuale non-surgettività di $μ_{A, B}$ quando $A, B$ sono fibrati in rette generati da sezioni globali e $\deg (A) + \deg (B) \geq 3 g - 1$ . Studiamo anche il caso $dim (Coker (μ_{A, B})) \geq 2$ .

Publié le : 2001-10-01

MR 1859428 | Zbl 1136.14021

@article{BUMI_2001_8_4B_3_677_0,
     author = {E. Ballico},
     title = {The rank of the multiplication map for sections of bundles on curves},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {677-683},
     zbl = {1136.14021},
     mrnumber = {1859428},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_3_677_0}
}

Ballico, E. The rank of the multiplication map for sections of bundles on curves. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 677-683. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_3_677_0/

Bibliographie

[AK] Altman, A.-Kleiman, S., Introduction to Grothendieck duality theory, Lect. Notes in Math., 146, Springer-Verlag, 1970. | MR 274461 | Zbl 0215.37201

[BR] Ballico, E.-Ramella, L., The restricted tangent bundle of smooth curves in Grassmannians and flag varieties, Rocky Mountains J. Math. (to appear). | MR 1810163 | Zbl 0996.14014

[Bu] Butler, D. C., Normal generation of vector bundles over a curve, J. Differ. Geom., 39 (1994), 1-34. | MR 1258911 | Zbl 0808.14024

[E] Eisenbud, D., Linear sections of determinantal varieties, Am. J. Math., 110 (1988), 541-575. | MR 944327 | Zbl 0681.14028

[EKS] Eisenbud, D.-Koh, J.-Stillman, M., Determinantal equations for curves of high degree, Amer. J. Math., 110 (1989), 513-540. | MR 944326 | Zbl 0681.14027

[G] Green, M., Koszul cohomology and the geometry of projective varieties, J. Differ. Geom., 19 (1984), 125-171. | MR 739785 | Zbl 0559.14008

[GL] Green-Lazarsfeld, R., On the projective normality of complete linear series on an algebraic curve, Invent. Math., 83 (1986), 73-90. | MR 813583 | Zbl 0594.14010

[La] Laumon, G., Fibrés vectoriels speciaux, Bull. Soc. Math. France, 119 (1991), 97-119. | MR 1101941 | Zbl 0741.14007

[N] Nagata, M., On selfintersection number of vector bundles of rank 2 on Riemann surface, Nagoya Math. J., 37 (1970), 191-196. | MR 258829 | Zbl 0193.21603

[NR] Narasimhan, M. S.-Ramanan, S., Deformations of the moduli space of vector bundles over an algebraic curve, Ann. of Math., 101 (1975), 391-417. | MR 384797 | Zbl 0314.14004

[Re] Re, R., Multiplication of sections and Clifford bounds for stable vector bundles, Comm. in Alg., 26 (1998), 1931-1944. | MR 1621712 | Zbl 0902.14024

[Su] Sundaram, N., Special divisors and vector bundles, Tôhoku Math. J., 39 (1987), 175-213. | MR 887936 | Zbl 0631.14021