Triangulated Endofunctors of the Derived Category of Coherent Sheaves Which Do Not Admit DG Liftings
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DOI: 10.1007/s40598-019-00114-x
Abstract: In, Rizzardo and Van den Bergh (An example of a non-Fourier–Mukai functor between derived categories of coherent sheaves. arXiv:1410.4039, 2014) constructed an example of a triangulated functor between the derived categories of coherent sheaves on… read more here.
Keywords: coherent sheaves; derived categories; triangulated endofunctors; functor ... See more keywords
Spherical T-duality and the spherical Fourier–Mukai transform
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DOI: 10.1016/j.geomphys.2018.07.020
Abstract: Abstract In Bouwknegt et al. (2015) [3, 4], we introduced spherical T-duality, which relates pairs of the form ( P , H ) consisting of an oriented S 3 -bundle P → M and a 7-cocycle… read more here.
Keywords: duality; mukai transform; spherical fourier; spherical duality ... See more keywords
Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic threefolds
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DOI: 10.1016/j.jalgebra.2022.03.042
Abstract: LO A BSTRACT . We focus on a class of Weierstraß elliptic threefolds that allows the base of the fibration to be a Fano surface or a numerically K -trivial surface. We define the notion… read more here.
Keywords: torsion free; slope stable; elliptic threefolds; stable torsion ... See more keywords
Fourier–Mukai Transform on a Compactified Jacobian
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DOI: 10.1093/imrn/rny136
Abstract: We use Fourier–Mukai transform to compute the cohomology of the Picard bundles on the compactified Jacobian of an integral nodal curve $Y$. We prove that the transform gives an injective morphism from the moduli space… read more here.
Keywords: vector bundles; mukai transform; space vector; moduli space ... See more keywords
Fourier–Mukai transform on Weierstrass cubics and commuting differential operators
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DOI: 10.1142/s0129167x18500647
Abstract: In this paper, we describe the spectral sheaves of algebras of commuting differential operators of genus one and rank two with singular spectral curve, solving a problem posed by Previato and Wilson. We also classify… read more here.
Keywords: mukai transform; weierstrass cubics; commuting differential; differential operators ... See more keywords
Baum–Connes and the Fourier–Mukai transform
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DOI: 10.1215/00192082-9725548
Abstract: The Baum-Connes map for finitely generated free abelian groups is a K-theoretic analogue of the Fourier-Mukai transform from algebraic geometry. We describe this K-theoretic transform in the language of topological correspondences, and compute its action… read more here.
Keywords: fourier mukai; connes fourier; baum connes; mukai transform ... See more keywords