Results 11 to 20 of about 382 (39)
Real quartic surfaces containing 16 skew lines
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 44, Page 2331-2345, 2004., 2004 It is well known that there is an open three‐dimensional subvariety Ms of the Grassmannian of lines in ℙ3 which parametrizes smooth irreducible complex surfaces of degree 4 which are Heisenberg invariant, and each quartic contains 32 lines but only 16 skew lines, being determined by its configuration of lines, are called a double 16.
Isidro Nieto
wiley +1 more source
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
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
core +2 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
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
doaj +1 more source
An inverse Grassmannian Littlewood–Richardson rule and extensions
Forum of Mathematics, SigmaChow rings of flag varieties have bases of Schubert cycles $\sigma _u $ , indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula for the structure constants of this basis.
Oliver Pechenik, Anna Weigandt
doaj +1 more source
Forum of Mathematics, SigmaIn our previous paper, we gave a presentation of the torus-equivariant quantum K-theory ring $QK_{H}(Fl_{n+1})$ of the (full) flag manifold $Fl_{n+1}$ of type $A_{n}$ as a quotient of a polynomial ring by an explicit ideal.
Toshiaki Maeno +2 more
doaj +1 more source
Borel-type presentation of the torus-equivariant quantum K-ring of flag manifolds of type C
Forum of Mathematics, SigmaWe give a presentation of the torus-equivariant (small) quantum K-ring of flag manifolds of type C as an explicit quotient of a Laurent polynomial ring; our presentation can be thought of as a quantization of the classical Borel presentation of the ...
Takafumi Kouno, Satoshi Naito
doaj +1 more source
Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups
, 2008 For the coinvariant rings of finite Coxeter groups of types other than H$_4$, we show that a homogeneous element of degree one is a strong Lefschetz element if and only if it is not fixed by any reflections.
A Borel +12 more
core +1 more source