ℙ-objects and autoequivalences of derived categories
By D. Huybrechts, Richard P. Thomas. 2005
94 citations recorded by the source corpus.
We describe new autoequivalences of derived categories of coherent sheaves arising from what we call ℙn-objects of the category. Standard examples arise from holomorphic symplectic manifolds. Under mirror symmetry these autoequivalences should be mirror to Seidel's Dehn twists about lagrangian ℙn submanifolds. We give various connections to spherical objects and spherical twists, and include a simple description of Atiyah and Kodaira-Spencer classes in an appendix.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8fa6cd27785d4a861b86b2b1176870b87b420a8b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Sabin Cautis
- D. Huybrechts
- Joel Kamnitzer
- Emanuele Macrì
- T. Bridgeland
- Nicolas Addington
- Anthony M. Licata
- P. Stellari
In Mathematical Physics
- Sabin Cautis
- Joel Kamnitzer
- D. Huybrechts
- T. Bridgeland
- Emanuele Macrì
- Nicolas Addington
- Anthony M. Licata
- Richard P. Thomas
Citations in the corpus
- Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes (2008, methodology): “This paper generalises [12,13] by working universally, using Fourier–Mukai kernels as in [5, 6 ].”
- Homological mirror symmetry for the genus two curve (2008, background): “For instance, many symplectic manifolds have rich automorphism groups arising from monodromy, and by thinking of those in terms of HMS, new classes of autoequivalences of derived categories have been discovered [57, 29, 31].”
- COHERENT SHEAVES AND CATEGORICAL sl2 ACTIONS (2009, methodology): “The idea to impose the existence of deformations was inspired by the work of Huybrechts-Thomas [ HT ] (see Remark 2.4).”
- New derived symmetries of some hyperkähler varieties (2011, background): “To get an autoequivalence of Db(S[n]) from our functor F , we are obliged to generalize Huybrechts and Thomas’s P-objects [20].”
- Derived categories of coherent sheaves (2006, background): “More recently, Huybrechts and Thomas [21] have studied projective space objects, which also give rise to autoequivalences.”