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Kazushi Ueda

  1. The special McKay correspondence and exceptional collection.

    Чт, 04/14/2011 - 15:01 — SomNambul
    Authors: Akira Ishii, Kazushi Ueda
    Subjects: Algebraic Geometry
    Abstract

    We 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.

  2. A note on homological mirror symmetry for singularities of type D.

    Пт, 04/02/2010 - 15:01 — SomNambul
    Authors: Kazushi Ueda, Masahiro Futaki
    Subjects: Symplectic Geometry
    Abstract

    We 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.

  3. Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space.

    Чт, 01/28/2010 - 16:01 — SomNambul
    Authors: Kazushi Ueda, Masahiro Futaki
    Subjects: Symplectic Geometry
    Abstract

    We 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.

  4. A-infinity categories associated with dimer models.

    Чт, 12/10/2009 - 16:01 — SomNambul
    Authors: Kazushi Ueda, Masahiro Futaki
    Subjects: Symplectic Geometry
    Abstract

    We 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.

  5. Homological mirror symmetry for Brieskorn-Pham singularities.

    Чт, 12/03/2009 - 16:01 — SomNambul
    Authors: Kazushi Ueda, Masahiro Futaki
    Subjects: Symplectic Geometry
    Abstract

    We 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.

  6. Dimer models and exceptional collections.

    Ср, 11/25/2009 - 16:01 — SomNambul
    Authors: Akira Ishii, Kazushi Ueda
    Subjects: Algebraic Geometry
    Abstract

    We 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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