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Polynomial interpolation problems in projective spaces and products of projective lines

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posted on 2017-06-02, 13:22 authored by Elisa Postinghel
These notes summarize part of my research work as a SAGA postdoctoral fellow. We study a class of polynomial interpolation problems which consists of determining the dimension of the vector space of homogeneous or multihomogeneous polynomials vanishing together with their partial derivatives at a finite set of general points. After translating the problem into the setting of linear systems in projective spaces or products of projective lines, we employ algebro-geometric techniques such as blowing-up and degenerations to calculate the dimension of such vector spaces. We compute the dimensions of linear systems with general points of any multiplicity in Pn in a family of cases for which the base locus is only linear [8]. Moreover we completely classify linear systems with double points in general position in products of projective lines (P1)n [26] and we relate this to the study of secant varieties of Segre-Veronese varieties.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

SAGA – Advances in ShApes, Geometry, and Algebra Geometry and Computing

Volume

10

Pages

199 - 216 (18)

Citation

POSTINGHEL, E., 2014. Polynomial interpolation problems in projective spaces and products of projective lines. IN: Dokken, T. and Muntingh, G. (eds.) SAGA – Advances in ShApes, Geometry, and Algebra: Results from the Marie Curie Initial Training Network, Cham: Springer, pp. 199-216.

Publisher

Springer International Publishing

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

Notes

This book chapter is in closed access.

ISBN

9783319086347

ISSN

1866-6795;1866-6809

Book series

Geometry and Computing;10

Language

  • en

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