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Title: Monads on projective varieties
Authors: Marchesi, S.
Marques, P. M.
Soares, H.
Keywords: Monads
ACM varieties
Issue Date: 2018
Publisher: Pacific Journal of Mathematics
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.
Peer reviewed: yes
DOI: 10.2140/pjm.2018.296.155
ISSN: 0030-8730
Accession number: WOS:000432892200008
Appears in Collections:BRU-RI - Artigos em revistas científicas internacionais com arbitragem científica

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