Kazushi Ueda
The special McKay correspondence and exceptional collection.
Thu, 04/14/2011 - 15:01 — SomNambulAuthors: Akira Ishii, Kazushi Ueda
Subjects: Algebraic Geometry
AbstractWe show that the derived category of coherent sheaves on the quotient stack
of the affine plane by a finite small subgroup of the general linear group is
obtained from the derived category of coherent sheaves on the minimal
resolution by adding a semiorthogonal summand with a full exceptional
collection.A note on homological mirror symmetry for singularities of type D.
Fri, 04/02/2010 - 15:01 — SomNambulAuthors: Kazushi Ueda, Masahiro Futaki
Subjects: Symplectic Geometry
AbstractWe prove homological mirror symmetry for Lefschetz fibrations obtained as
disconnected sums of polynomials of types A or D. The proof is based on the
behavior of the Fukaya category under the addition of a polynomial of type D.Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space.
Thu, 01/28/2010 - 16:01 — SomNambulAuthors: Kazushi Ueda, Masahiro Futaki
Subjects: Symplectic Geometry
AbstractWe introduce the notion of a tropical coamoeba which gives a combinatorial
description of the Fukaya category of the mirror of a toric Fano stack. We show
that the polyhedral decomposition of a real n-torus into (n + 1) permutohedra
gives a tropical coamoeba for the mirror of the projective space, and use it to
prove a torus-equivariant version of homological mirror symmetry for the
projective space. As a corollary, we obtain homological mirror symmetry for
toric orbifolds of the projective space.A-infinity categories associated with dimer models.
Thu, 12/10/2009 - 16:01 — SomNambulAuthors: Kazushi Ueda, Masahiro Futaki
Subjects: Symplectic Geometry
AbstractWe associate an A-infinity category with a dimer model, and show that it is
derived-equivalent to the category of representations of the quiver with
relations associated with the dimer model if the dimer model is consistent. We
also associate an exact Lefschetz fibration with a pair of a dimer model and an
internal perfect matching on it, and use it to prove a version of homological
mirror symmetry for two-dimensional toric Fano stacks.Homological mirror symmetry for Brieskorn-Pham singularities.
Thu, 12/03/2009 - 16:01 — SomNambulAuthors: Kazushi Ueda, Masahiro Futaki
Subjects: Symplectic Geometry
AbstractWe prove that the derived Fukaya category of the Lefschetz fibration defined
by a Brieskorn-Pham polynomial is equivalent to the triangulated category of
singularities associated with the same polynomial together with a grading by an
abelian group of rank one. Symplectic Picard-Lefschetz theory developed by
Seidel is an essential ingredient of the proof.Dimer models and exceptional collections.
Wed, 11/25/2009 - 16:01 — SomNambulAuthors: Akira Ishii, Kazushi Ueda
Subjects: Algebraic Geometry
AbstractWe construct a full strong exceptional collection consisting of line bundles
on any two-dimensional smooth toric weak Fano stack. The total endomorphism
algebra of the resulting collection is isomorphic to the path algebra of a
quiver with relations associated with a dimer model and a perfect matching on
it.
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