Complex surfaces with equivalent derived categories
By T. Bridgeland, Antony Maciocia. 2001
135 citations recorded by the source corpus.
Abstract. We examine the extent to which a smooth minimal complex projective surface X is determined by its derived category of coherent sheaves (DX). To do this we find, for each such surface X, the set of surfaces Y for which there exists a Fourier-Mukai transform D $(Y)\to$ D(X).
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2111411fca353abef2e7933f612d337f1bd2c063
How researchers see this paper
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In Algebra and Number Theory
- D. Huybrechts
- P. Stellari
- Sukhendu Mehrotra
- Hokuto Uehara
- L. Hille
- R. Mir'o-Roig
- Michel van den Bergh
- Keiji Oguiso
In Geometry and Topology
- Emanuele Macrì
- D. Huybrechts
- P. Stellari
- Arend Bayer
- Keiji Oguiso
- Yukinobu Toda
- Sukhendu Mehrotra
- T. Bridgeland
Citations in the corpus
- D-Equivalence and K-Equivalence (2002, background): “We shall provide a partial answer to the above problem in this paper.”
- K3 surfaces via almost-primes (2001, background): “See also [ BM 1 , 2], [Cl], [Th] for further progress and relevant work.”
- Handbook of Tilting Theory: Fourier-Mukai transforms (2004, background): “The possible non-trivial Fourier-Mukai partners for minimal surfaces were classified by Bridgeland and Maciocia in [17].”
- Lectures on K3 Surfaces (2016, methodology): “We sketch the argument due to Bridgeland and Maciocia [85] for complex projective K3 surfaces.”
- Inducing stability conditions (2007, methodology): “2 we improve the derived version of the Torelli Theorem for Enriques surfaces (see [13]) and relate the topology of the connected component just introduced to the description of the group of autoequivalences.”
- Equivariant autoequivalences for finite group actions (2005, background): “(2) Considering only birational equivalence classes of Hilbert schemes on K3 surfaces, we find that each such class is finite, since K3 surfaces have only finitely many Fourier-Mukai partners [4].”
- Tilting sheaves on toric varieties (2004, background): “an equivalence of categories φ : D b (Y ) → D b (X) preserving the triangles (for more information see [8], [9] and [ 11 ]).”
- Equivalences of twisted K3 surfaces (2004, result): “The untwisted case of this corollary had been proved in [ 5 ].”
- Autoequivalences of derived categories on the minimal resolutions of An-singularities on surfaces (2004, background): “Because S is of general type and �(Ox) ⊗ ωS ∼ �(Ox) for any x ∈ S (see [ BM01 ,”