6533b7d1fe1ef96bd125cb6a

RESEARCH PRODUCT

Derived categories of irreducible projective curves of arithmetic genus one

Bernd KreußlerIgor Burban

subject

Discrete mathematicsDerived categoryPure mathematicsAlgebra and Number TheoryFourier–Mukai transformGroup (mathematics)Moduli spaceCoherent sheafMathematics::Algebraic GeometryMathematics::Category TheoryBounded functionArithmetic genusAlgebraic curveMathematics

description

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.

https://doi.org/10.1112/s0010437x06002090