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On spherical nilpotent orbits and beyond

Dmitri I. Panyushev (1999)

Annales de l'institut Fourier

We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s θ -groups. This yields a description of spherical...

On symmetric semialgebraic sets and orbit spaces

Ludwig Bröcker (1998)

Banach Center Publications

For a symmetric (= invariant under the action of a compact Lie group G) semialgebraic basic set C, described by s polynomial inequalities, we show, that C can also be written by s + 1 G-invariant polynomials. We also describe orbit spaces for the action of G by a number of inequalities only depending on the structure of G.

On tangent cones to Schubert varieties in type E

Mikhail V. Ignatyev, Aleksandr A. Shevchenko (2020)

Communications in Mathematics

We consider tangent cones to Schubert subvarieties of the flag variety G / B , where B is a Borel subgroup of a reductive complex algebraic group G of type E 6 , E 7 or E 8 . We prove that if w 1 and w 2 form a good pair of involutions in the Weyl group W of G then the tangent cones C w 1 and C w 2 to the corresponding Schubert subvarieties of G / B do not coincide as subschemes of the tangent space to G / B at the neutral point.

On the canonical ideal of a set of points

Martin Kreuzer (2000)

Bollettino dell'Unione Matematica Italiana

Dato un insieme X di s punti nello spazio proiettivo, si costruisce un esplicito ideale canonico I nel suo anello di coordinate R . Si descrivono le componenti omogenee di I e la struttura della mappa di moltiplicazione R σ ⊗ I σ + 1 → I 2 ⁢ σ + 1 , dove σ = max ⁡ i ∣ H X ⁢ i < s . Tra le applicazioni ci sono varie caratterizzazioni di insiemi di punti coomologicamente uniformi, disuguaglianze nelle loro funzioni di Hilbert, il calcolo del primo modulo delle sizigie di I in casi particolari, una generalizzazione della «trasformata di Gale» a trasformate...

On the class of some projective varieties.

Edoardo Ballico, Marina Bertolini, Cristina Turrini (1997)

Collectanea Mathematica

Some inequalities between the class and the degree of a smooth complex projective manifold are given. Application to the case of low sectional genus are supplied.

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