Rank 4 vector bundles on the quintic threefold

• Autorzy: Carlo Madonna
• Języki publikacji: EN

Abstrakty

EN

By the results of the author and Chiantini in [3], on a general quintic threefold X⊂P 4 the minimum integer p for which there exists a positive dimensional family of irreducible rank p vector bundles on X without intermediate cohomology is at least three. In this paper we show that p≤4, by constructing series of positive dimensional families of rank 4 vector bundles on X without intermediate cohomology. The general member of such family is an indecomposable bundle from the extension class Ext 1 (E, F), for a suitable choice of the rank 2 ACM bundles E and F on X. The existence of such bundles of rank p=3 remains under question.

Słowa kluczowe

EN

ACM bundles; quintic threefold; 14J60

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 3
• Strony: 404-411

Daty

wydano

2005-09-01

online

2005-09-01

Twórcy

autor

Carlo Madonna

• Università degli Studi di Roma “La Sapienza”

Bibliografia

• [1] E. Arrondo and L. Costa: “Vector bundles on Fano 3-folds without intermediate cohomology”, Comm. Algebra, Vol. 28, (2000), pp. 3899–3911.
• [2] R.O. Buchweitz, G.M. Greuel and F.O. Schreyer: “Cohen-Macaulay modules on hypersurface singularities II”, Invent. Math., Vol. 88, (1987), pp. 165–182. http://dx.doi.org/10.1007/BF01405096
• [3] L. Chiantini and C. Madonna: “ACM bundles on a general quintic threefold”, Matematiche (Catania), Vol. 55, (2000), pp. 239–258.
• [4] R. Hartshorne: “Stable vector bundles of rank 2 on ℙ3”, Math. Ann., Vol. 238, (1978), pp. 229–280. http://dx.doi.org/10.1007/BF01420250
• [5] S. Katz and S. Stromme: Schubert, a Maple package for intersection theory and enumerative geometry, from website http://www.mi.uib.no/schubert/
• [6] C.G. Madonna: “ACM bundles on prime Fano threefolds and complete intersection Calabi Yau threefolds”, Rev. Roumaine Math. Pures Appl., Vol. 47, (2002), pp. 211–222.
• [7] C. Okonek, M. Schneider and H. Spindler: “Vector bundles on complex projective spaces”, Progress in Mathematics, Vol. 3, (1980), pp. 389.

Identyfikatory

DOI

10.2478/BF02475915