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Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties

Published online by Cambridge University Press:  20 November 2018

A. Bernardi ,
M. V. Catalisano ,
A. Gimigliano  and
M. Idà
A. Bernardi
Affiliation:
Dipartimento di Matematica di Bologna, Porta San Donato 5, 40126, Bologna, Italia email: abernardi@dm.unibo.it
M. V. Catalisano
Affiliation:
DIPTEM, Università di Genova, Genova, Italia email: catalisano@dimet.unige.it
A. Gimigliano
Affiliation:
Dipartimento di Matematica and C.I.R.A.M., Università di Bologna, Bologna, Italia email: gimiglia@dm.unibo.it
M. Idà
Affiliation:
Dipartimento di Matematica, Università di Bologna, Bologna, Italia email: ida@dm.unibo.it
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Abstract

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We consider the $k$-osculating varieties ${{O}_{k,\,n.d}}$ to the (Veronese) $d$-uple embeddings of ${{\mathbb{P}}^{n}}$. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes $Y\,\subset \,{{\mathbb{P}}^{n}}$ to $O_{k,n,d}^{s}$ and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.

Keywords

14N1515A69
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 3 , 01 June 2007 , pp. 488 - 502
Copyright
Copyright © Canadian Mathematical Society 2007

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