Tom Bridgeland
An introduction to motivic Hall algebras.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: Tom Bridgeland
Subjects: Algebraic Geometry
AbstractWe give an introduction to Joyce's construction of the motivic Hall algebra
of coherent sheaves on a variety M. When M is a Calabi-Yau threefold we define
a semi-classical integration map from a Poisson subalgebra of this Hall algebra
to the ring of functions on a symplectic torus. This material will be used in
arxiv:1002.4374 to prove some basic properties of Donaldson-Thomas
curve-counting invariants on Calabi-Yau threefolds.Hall algebras and curve-counting invariants.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: Tom Bridgeland
Subjects: Algebraic Geometry
AbstractWe use Joyce's theory of motivic Hall algebras to prove that reduced
Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide
with stable pair invariants, and that the generating functions for these
invariants are Laurent expansions of rational functions.Helices on del Pezzo surfaces and tilting Calabi-Yau algebras.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Tom Bridgeland, David Stern
Subjects: Rings and Algebras
AbstractWe study tilting for a class of Calabi-Yau algebras associated to helices on
Fano varieties. We do this by relating the tilting operation to mutations of
exceptional collections. For helices on del Pezzo surfaces the algebras are of
dimension three, and using an argument of Herzog, together with results of
Kuleshov and Orlov, we obtain a complete description of the tilting process in
terms of quiver mutations.Helices on del Pezzo surfaces and tilting Calabi-Yau algebras.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Tom Bridgeland, David Stern
Subjects: Rings and Algebras
AbstractWe study tilting for a class of Calabi-Yau algebras associated to helices on
Fano varieties. We do this by relating the tilting operation to mutations of
exceptional collections. For helices on del Pezzo surfaces the algebras are of
dimension three, and using an argument of Herzog, together with results of
Kuleshov and Orlov, we obtain a complete description of the tilting process in
terms of quiver mutations.
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