Sheaves on Spaces
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Instanton sheaves on complex projective spaces
We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of modu...
متن کاملPerverse Coherent Sheaves on Blow-up. Ii. Wall-crossing and Betti Numbers Formula
This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up p : X̂ → X of a projective surface X at a point 0. The followings are main results of this paper: a) We describe the wall-crossing between moduli spaces caused by twisting of the line bundle O(C) associated with the exceptional diviso...
متن کاملSome Examples of Isomorphisms Induced by Fourier-mukai Functors
In order to investigate sheaves on abelian varieties, Mukai [Mu1] introduced a very powerful tool called Fourier-Mukai functor. As an application, Mukai ([Mu1], [Mu4]) computed some moduli spaces of stable sheaves on abelian varieties. Recently, Dekker [D] found some examples of isomorphisms of moduli spaces of sheaves induced by Fourier-Mukai functors. As an application, he proved that moduli ...
متن کاملFixed Point Loci of Moduli Spaces of Sheaves on Toric Varieties
Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves on an arbitrary nonsingular toric variety X. This combinatorial description can be used to construct very explicit moduli spaces of stable equivariant sheaves on X using Geometric Invariant Theory (analogous to techniques used in case of equivariant vector bundles by Payne and Perling). We...
متن کاملModuli spaces of framed instanton sheaves on projective spaces
We introduce a generalization of the Atiyah-Drinfeld-Hitchin-Manin linear algebraic data and a generalization of Atiyah-Drinfeld-Hitchin-Manin equation, which are subsequently used to construct all framed instanton bundles on complex projective spaces. Using geometric invariant theory, we prove that the moduli spaces of framed instanton sheaves is a quasiprojective variety. We also provide a li...
متن کاملPerverse Sheaves on Image Multiple Point Spaces
Using multiple point spaces some new examples of perverse sheaves on images of maps are described. Furthermore, suppose f : X ! Y is a nite and proper map of complex analytic manifolds of dimension n and n + 1 such that every multiple point space is non-singular and has the dimension expected of a generic map. Then we can describe the composition series for the constant sheaf on the image in th...
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تاریخ انتشار 2015