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Marchesi, S., Marques, P. M. & Soares, H. (2018). Monads on projective varieties. Pacific Journal of Mathematics. 296 (1), 155-180

S. Marchesi et al.,  "Monads on projective varieties", in Pacific Journal of Mathematics, vol. 296, no. 1, pp. 155-180, 2018

@article{marchesi2018_1714780869896,
	author = "Marchesi, S. and Marques, P. M. and Soares, H.",
	title = "Monads on projective varieties",
	journal = "Pacific Journal of Mathematics",
	year = "2018",
	volume = "296",
	number = "1",
	doi = "10.2140/pjm.2018.296.155",
	pages = "155-180",
	url = "https://msp.org/pjm/"
}

TY  - JOUR
TI  - Monads on projective varieties
T2  - Pacific Journal of Mathematics
VL  - 296
IS  - 1
AU  - Marchesi, S.
AU  - Marques, P. M.
AU  - Soares, H.
PY  - 2018
SP  - 155-180
SN  - 0030-8730
DO  - 10.2140/pjm.2018.296.155
UR  - https://msp.org/pjm/
AB  - 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.
ER  -