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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

MONADS ON PROJECTIVE VARIETIES

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Author(s):
Marchesi, Simone [1] ; Marques, Pedro Macias [2] ; Soares, Helena
Total Authors: 3
Affiliation:
[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Cidade Univ Zeferino Vaz, Campinas, SP - Brazil
[2] Univ Evora, Inst Invest & Formacao Avancada, Ctr Invest Matemat & Aplicacoes, Dept Matemat, Escola Ciencias & Tecnol, Evora - Portugal
Total Affiliations: 2
Document type: Journal article
Source: PACIFIC JOURNAL OF MATHEMATICS; v. 296, n. 1, p. 155-180, SEP 2018.
Web of Science Citations: 0
Abstract

We generalize Floystad's theorem on the existence of monads on projective space to a larger set of projective varieties. We consider a variety X, a line bundle L on X, and a basepoint-free linear system of sections of L giving a morphism to projective space whose image is either arithmetically Cohen-Macaulay (ACM) or linearly normal and not contained in a quadric. We give necessary and sufficient conditions on integers a, b and c for a monad of type 0 -> (L-v)(a)-> O-X(b) -> L-c -> 0 to exist. We show that under certain conditions there exists a monad whose cohomology sheaf is simple. We furthermore characterize low-rank vector bundles that are the cohomology sheaf of some monad as above. Finally, we obtain an irreducible family of monads over projective space and make a description on how the same method could be used on an ACM smooth projective variety X. We establish the existence of a coarse moduli space of low-rank vector bundles over an odd-dimensional X and show that in one case this moduli space is irreducible. (AU)

FAPESP's process: 14/12558-9 - Monads on projective varieties, syzygy bundles and Gorenstein Artin algebras
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 14/00498-1 - Generalized instanton bundles on smooth projective varieties
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 17/03487-9 - Vector bundles: from the instanton family to a new regularity
Grantee:Simone Marchesi
Support Opportunities: Regular Research Grants