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Title: Polynomial interpolation problems in projective spaces and products of projective lines
Authors: Postinghel, Elisa
Issue Date: 2014
Publisher: Springer International Publishing
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.
Series/Report no.: Geometry and Computing;10
Abstract: 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.
Description: This book chapter is in closed access.
Version: Accepted for publication
DOI: 10.1007/978-3-319-08635-4_11
URI: https://dspace.lboro.ac.uk/2134/25241
Publisher Link: http://dx.doi.org/10.1007/978-3-319-08635-4_11
ISBN: 9783319086347
ISSN: 1866-6795
Appears in Collections:Closed Access (Maths)

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