Deformations and Fourier-Mukai transforms
By Yukinobu Toda. 2005
59 citations recorded by the source corpus.
The aim of this paper is twofold: First we give an explicit construction of the infinitesimal deformations of the category Coh(X) of coherent sheaves on a smooth projective variety X. Secondly we show that any Fourier-Mukai transform $/Phi/colon D^b(X)/to D^b(Y)$ extends to an equivalence between the derived categories of the deformed Abelian categories.
Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d808bf10229a6c1d31d06313469916b86bfc9d24
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Emanuele Macrì
- P. Stellari
- D. Huybrechts
- Kieran G. O’Grady
- E. Markman
- Justin Sawon
- A. Rapagnetta
- Misha Verbitsky
In Geometry and Topology
- P. Stellari
- Emanuele Macrì
- D. Huybrechts
- Arend Bayer
- Chunyi Li
- Alexander Kuznetsov
- E. Markman
- Benjamin Schmidt
In Statistical and Nonlinear Physics
Citations in the corpus
- Derived equivalences of K3 surfaces and orientation (2007, methodology): “The proof given in [34] generalizes in a straightforward way.”
- Hodge theory and derived categories of cubic fourfolds (2012, unknown): “We are guided by the deformation theory for Fourier-Mukai equivalences in the wonderful papers [41, 23] 5 but with a number of simplifications and one generalisation (to Fourier-Mukai functors which are only fully faithful).”
- The K3 category of a cubic fourfold (2015, methodology): “Due to a result of Toda [Tod09] (cf. [AT14, Theorem 7.1]) it suffices to show that under HH 2(X ′) // Ext2X′×X(P, P ) respectively HH 2(X) // Ext2X′×X(P, P ) the classes κX′ and κX are mapped to the same class.”