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Here we give conditions and examples for the surjectivity or injectivity of the restriction map , where is a projective variety, is a vector bundle on and is a “general” -dimensional subscheme of , union of general “fat points”.
Soit une variété algébrique projective lisse irréductible. On appelle variété de modules fins de faisceaux sur une famille de faisceaux cohérents sur paramétrée par une variété intègre , possédant les propriétés suivantes : est plate sur ; pour tous distincts, les faisceaux et sur ne sont pas isomorphes et est une déformation complète de ; enfin possède une propriété universelle locale évidente. On a aussi la notion de variété de modules fins définie localement, où est...
We study relatively semi-stable vector bundles and their moduli on non-Kähler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-Kähler elliptic principal bundle over a primary Kodaira surface are computed.
In this article, we develop a geometric method to construct solutions of the classical Yang–Baxter equation, attaching a family of classical -matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic -matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained solutions are rational and compute them explicitly. We also describe them in terms of Stolin’s classication and prove...
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