Results 1 to 10 of about 367 (29)
Frobenius splitting of Schubert varieties of semi-infinite flag manifolds
Forum of Mathematics, Pi, 2021 We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field ${\mathbb K}$ of characteristic $\neq 2$ from scratch.
Syu Kato
doaj +1 more source
Inverse K-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Forum of Mathematics, Sigma, 2021 We prove an explicit inverse Chevalley formula in the equivariant K-theory of semi-infinite flag manifolds of simply laced type. By an ‘inverse Chevalley formula’ we mean a formula for the product of an equivariant scalar with a Schubert class, expressed
Takafumi Kouno +3 more
doaj +1 more source
Decomposition of homogeneous polynomials with low rank [PDF]
, 2010 Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$-th secant varieties of the standard Veronese variety $X_{m,d}\subset \mathbb{P}^
A. Bernardi +15 more
core +6 more sources
Apolarity, Hessian and Macaulay polynomials [PDF]
, 2012 A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b.
Alexander J. +12 more
core +2 more sources
Gromov-Witten invariants on Grassmannians [PDF]
, 2003 We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the two-step
Buch, Anders Skovsted +2 more
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An inequality of Kostka numbers and Galois groups of Schubert problems [PDF]
, 2012 We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kostka ...
Brooks, Christopher J. +2 more
core +7 more sources
The Degree of the Tangent and Secant Variety to a Projective Surface [PDF]
, 2019 In this paper we present a way of computing the degree of the secant (resp., tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is $3$-very ample.
Cattaneo, Andrea
core +3 more sources
Positivity of Thom polynomials II: the Lagrange singularities [PDF]
, 2009 We show that Thom polynomials of Lagrangian singularities have nonnegative coefficients in the basis consisting of Q-functions. The main tool in the proof is nonnegativity of cone classes for globally generated bundles.Comment: 16 pages, reduced ...
Mikosz, Malgorzata +2 more
core +1 more source
, 2015 We prove that the general fibre of the $i$-th Gauss map has dimension $m$ if and only if at the general point the $(i+1)$-th fundamental form consists of cones with vertex a fixed $\mathbb P^{m-1}$, extending a known theorem for the usual Gauss map.
De Poi, Pietro, Ilardi, Giovanna
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Infinite flags and Schubert polynomials
Forum of Mathematics, SigmaWe study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched ...
David Anderson
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