NDLI: Generalized varieties of sums of powers

Content Provider	Springer Nature Link
Author	Massarenti, Alex
Copyright Year	2016
Abstract	Let X ⊂ PN be an irreducible, non-degenerate variety. The generalized variety of sums of powers V S P H X(h) of X is the closure in the Hilbert scheme Hilbh (X) of the locus parametrizing collections of points {x 1,..., x h} such that the (h -1)-plane >x 1,..., x h> passes through a fixed general point p ∈ PN. When X = V d n is a Veronese variety we recover the classical variety of sums of powers V S P(F, h) parametrizing additive decompositions of a homogeneous polynomial as powers of linear forms. In this paper we study the birational behavior of V S P H X(h). In particular, we show how some birational properties, such as rationality, unirationalityand rational connectedness, of V S P H X(h) are inherited from the birational geometry of variety X itself.
Ending Page	934
Page Count	24
Starting Page	911
File Format	PDF
ISSN	16787544
e-ISSN	16787714
Journal	Bulletin of the Brazilian Mathematical Society
Issue Number	3
Volume Number	47
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-02-24
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fibrations, degenerations Rationality questions Rational and unirational varieties rational varieties Stacks and moduli problems Theoretical, Mathematical and Computational Physics varieties of sums of powers Projective techniques Mathematics Rationally connected varieties rationally connected varieties
Content Type	Text
Resource Type	Article
Subject	Mathematics

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