Главная

Ravi Vakil

  1. Solving Schubert Problems with Littlewood-Richardson Homotopies.

    Втр, 01/26/2010 - 16:01 — SomNambul
    Authors: Frank Sottile, Ravi Vakil, Jan Verschelde
    Subjects: Numerical Analysis
    Abstract

    We present a new numerical homotopy continuation algorithm for finding all
    solutions to Schubert problems on Grassmannians. This Littlewood-Richardson
    homotopy is based on Vakil's geometric proof of the Littlewood-Richardson rule.
    Its start solutions are given by linear equations and they are tracked through
    a sequence of homotopies encoded by certain checker configurations to find the
    solutions to a given Schubert problem. For generic Schubert problems the number
    of paths tracked is optimal.

  2. The ideal of relations for the ring of invariants of n points on the line.

    Пт, 09/18/2009 - 11:36 — SomNambul
    Authors: Andrew Snowden, Ben Howard, John Millson, Ravi Vakil
    Subjects: Algebraic Geometry
    Abstract

    The study of the projective coordinate ring of the (geometric invariant
    theory) moduli space of n ordered points on P^1 up to automorphisms began with
    Kempe in 1894, who proved that the ring is generated in degree one in the main
    (n even, unit weight) case. We describe the relations among the invariants for
    all possible weights. In the main case, we show that up to the symmetric group
    symmetry, there is a single equation. For n not 6, it is a simple quadratic
    binomial relation.

  3. The ideal of relations for the ring of invariants of n points on the line.

    Пт, 09/18/2009 - 11:36 — SomNambul
    Authors: Andrew Snowden, Ben Howard, John Millson, Ravi Vakil
    Subjects: Algebraic Geometry
    Abstract

    The study of the projective coordinate ring of the (geometric invariant
    theory) moduli space of n ordered points on P^1 up to automorphisms began with
    Kempe in 1894, who proved that the ring is generated in degree one in the main
    (n even, unit weight) case. We describe the relations among the invariants for
    all possible weights. In the main case, we show that up to the symmetric group
    symmetry, there is a single equation. For n not 6, it is a simple quadratic
    binomial relation.

  4. The ideal of relations for the ring of invariants of n points on the line: integrality results.

    Пт, 09/18/2009 - 11:36 — SomNambul
    Authors: Andrew Snowden, Ben Howard, John Millson, Ravi Vakil
    Subjects: Algebraic Geometry
    Abstract

    Consider the projective coordinate ring of the GIT quotient (P^1)^n//SL(2),
    with the usual linearization, where n is even. In 1894, Kempe proved that this
    ring is generated in degree one. In [HMSV2] we showed that, over the rationals,
    the relations between degree one invariants are generated by a class of
    quadratic relations -- the simplest binomial relations -- with the exception of
    n=6, where there is a single cubic relation. The purpose of this paper is to
    show that these results hold over Z[1/12!], and to suggest why they may be true
    over Z[1/6].

  5. The ideal of relations for the ring of invariants of n points on the line: integrality results.

    Пт, 09/18/2009 - 11:36 — SomNambul
    Authors: Andrew Snowden, Ben Howard, John Millson, Ravi Vakil
    Subjects: Algebraic Geometry
    Abstract

    Consider the projective coordinate ring of the GIT quotient (P^1)^n//SL(2),
    with the usual linearization, where n is even. In 1894, Kempe proved that this
    ring is generated in degree one. In [HMSV2] we showed that, over the rationals,
    the relations between degree one invariants are generated by a class of
    quadratic relations -- the simplest binomial relations -- with the exception of
    n=6, where there is a single cubic relation. The purpose of this paper is to
    show that these results hold over Z[1/12!], and to suggest why they may be true
    over Z[1/6].

Math-arch

RSS-материал