Derived categories of irreducible projective curves of arithmetic genus one

By I. Burban, Bernd Kreußler. Compositio Mathematica, 2005

54 citations recorded by the source corpus.

We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all $t$-structures of this category is given. We describe the moduli space of stability conditions, obtain a complete classification of all spherical objects in this category and show that the group of exact auto-equivalences acts transitively on them. Harder–Narasimhan filtrations in the sense of Bridgeland are used as our main technical tool.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/18dc67e93e432307e08894e32e5ad51912a64183

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

1. P. Aspinwall
2. G. Moore
3. T. Bridgeland
4. Yukinobu Toda
5. A. Kapustin
6. G. Segal
7. Balázs Szendrői
8. Mark Gross

In Statistical and Nonlinear Physics

1. G. Moore
2. P. Aspinwall
3. Balázs Szendrői
4. Michael R Douglas
5. G. Segal
6. T. Bridgeland
7. Mark Gross
8. Alastair Craw

Citations in the corpus

• Flat surfaces and stability structures (2014, unknown): “The space of stability conditions on Db(E) was computed by Burban–Kreußler [17].”
• Dirichlet Branes and Mirror Symmetry (2009, background): “In [78], the case of irreducible singular curves of arithmetic genus one was treated, again obtaining (5.”
• Relative integral functors for singular fibrations and singular partners (2006, background): “[5] A. Bondal and D. Orlov, Derived categories of coherent sheaves, in Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), Beijing, 2002, Higher Ed.”