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Singularities of hyperdeterminants

Jerzy Weyman, Andrei Zelevinsky (1996)

Annales de l'institut Fourier

We study the singular locus of the variety of degenerate hypermatrices of an arbitrary format. Our main result is a classification of irreducible components of the singular locus. Equivalently, we classify irreducible components of the singular locus for the projectively dual variety of a product of several projective spaces taken in the Segre embedding.

Slices étales

Domingo Luna (1973)

Mémoires de la Société Mathématique de France

Smooth components of Springer fibers

William Graham, R. Zierau (2011)

Annales de l’institut Fourier

This article studies components of Springer fibers for 𝔤𝔩 ( n ) that are associated to closed orbits of G L ( p ) × G L ( q ) on the flag variety of G L ( n ) , n = p + q . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of G L ( n ) . We prove that if is a line bundle on the flag variety associated to a dominant weight, then the higher...

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