Semi-orthogonal decomposability of the derived category of a curve
By Shinnosuke Okawa. 2011
54 citations recorded by the source corpus.
Abstract We show that the bounded derived category of coherent sheaves on a smooth projective curve except the projective line admits no non-trivial semi-orthogonal decompositions.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1bb73bfad97d4f2c80c8e57d62ba0ddf17e09f4e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Alexander Perry
- Christian Bohning
- Hans-Christian Graf von Bothmer
- Alexander Kuznetsov
- Pawel Sosna
- Yuri Prokhorov
- Constantin Shramov
- Nicolas Addington
In Geometry and Topology
- Alexander Kuznetsov
- Alexander Perry
- Christian Bohning
- Hans-Christian Graf von Bothmer
- Pawel Sosna
- K. Hori
- Emanuele Macrì
- P. Stellari
Citations in the corpus
- On the derived category of the classical Godeaux surface (2012, background): “Furthermore, varieties of general type with globally generated canonical bundle do not have exceptional objects, see [27].”
- Derived Categories View on Rationality Problems (2015, background): “D(k) is indecomposable. Proof. Indeed, SD(k) = id, so it is Calabi–Yau of dimension 0. Besides, one can check that derived categories of curves of positive genus are indecomposable. Proposition 2.23 ([Oka11]). Let T = D(C) with C a smooth projective curve. If g(C) > 0 then T is indecomposable. If”
- Derived categories of Gushel–Mukai varieties (2016, background): “Further, by [47] any category of geometric dimension 1 is equivalent to the derived category of a curve.”
- Semiorthogonal decompositions in algebraic geometry (2014, background): “[44]) is based on special properties of categories of homological dimension 1.”