Displaying 441 – 460 of 1240

Showing per page

Higher order duality and toric embeddings

Alicia Dickenstein, Sandra Di Rocco, Ragni Piene (2014)

Annales de l’institut Fourier

The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the...

Hilbert series of the Grassmannian and k -Narayana numbers

Lukas Braun (2019)

Communications in Mathematics

We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the q -Hilbert series is a Vandermonde-like determinant. We show that the h -polynomial of the Grassmannian coincides with the k -Narayana polynomial. A simplified formula for the h -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the k -Narayana numbers, i.e. the h -polynomial...

How to draw tropical planes.

Herrmann, Sven, Jensen, Anders, Joswig, Michael, Sturmfels, Bernd (2009)

The Electronic Journal of Combinatorics [electronic only]

Currently displaying 441 – 460 of 1240