منابع مشابه
Deformations and Fourier-Mukai transforms
The aim of this paper is the following: Firstly give the explicit constructions of the infinitesimal deformation of Coh(X). Here X is a smooth projective variety. Secondly we show the Fourier-Mukai transform Φ: D(X) → D(Y ) extends to an equivalence between the derived categories of the deformed categories.
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Let X be a smooth projective variety. We study a relationship between the derived category of X and that of a canonical divisor. As an application, we will study FourierMukai transforms when κ(X) = dimX − 1.
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We prove Atiyah's classi cation results about indecomposable vector bundles on an elliptic curve by applying the Fourier-Mukai transform. We extend our considerations to semistable bundles and construct the universal stable sheaves. MSC 2000: 14H60 Vector bundles on curves and their moduli, 14H52 Elliptic curves.
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Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi–Yau manifold Y should act by families of Fourier–Mukai transforms over the complex moduli space of the mirror X. The conjecture generalizes a proposal of Kontsevich relating monodromy transformations and selfequivalences. Supporting evidence is given in the case of ...
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Let X be a smooth 3-fold whose kodaira dimension is positive. The main purpose of this paper is to investigate the set of smooth projective varieties Y whose derived categories of coherent sheaves are equivalent to that of X as triangulated categories. If there exists an equivalence Φ: D(X)→ D(Y ) we can compare derived categories of canonical divisors of X and Y , and this gives an inductive t...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2009
ISSN: 0022-040X
DOI: 10.4310/jdg/1228400631