Marchesi, SimoneMarques, Pedro MacíasSoares, Helena2019-10-232019-10-232018-05-010030-8730https://hdl.handle.net/2445/142819We generalize Fløystad's theorem on the existence of monads on projectivespace to a larger set of projective varieties. We consider a varietyX, a linebundleLonX, and a basepoint-free linear system of sections ofLgiving amorphism to projective space whose image is either arithmetically Cohen-Macaulay (ACM) or linearly normal and not contained in a quadric. Wegive necessary and sufficient conditions on integersa,bandcfor a monadof type $\mathbf{0} \rightarrow\left(\boldsymbol{L}^{\vee}\right)^{a} \rightarrow \mathcal{O}_{X}^{b} \rightarrow \boldsymbol{L}^{c} \rightarrow \mathbf{0}$ to exist. We show that under certain conditions there exists a monad whosecohomology sheaf is simple. We furthermore characterize low-rank vectorbundles that are the cohomology sheaf of some monad as above.Finally, we obtain an irreducible family of monads over projective spaceand make a description on how the same method could be used on an ACMsmooth projective varietyX. We establish the existence of a coarse modulispace of low-rank vector bundles over an odd-dimensionalXand show thatin one case this moduli space is irreducible.26 p.application/pdfeng(c) Mathematical Sciences Publishers (MSP), 2018Geometria algebraicaVarietats algebraiquesAlgebraic geometryAlgebraic varietiesinfo:eu-repo/semantics/article6921602019-10-23info:eu-repo/semantics/openAccess