Some defective secant varieties to osculating varieties of Veronese surfaces

Alessandra Bernardi 1 Maria Virgina Catalisano 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We consider the $k$-osculating varieties $O_{k,d}$ to the Veronese $d-$uple embeddings of $\PP 2$. By studying the Hilbert function of certain zero-\-dimensional schemes $Y\subset \PP 2$, we find the dimension of $O^s_{k,d}$, the $(s-1)^{th}$secant varieties of $O_{k,d}$, for $3 \leq s\leq 6$ and $s=9$, and we determine whether those secant varieties are defective or not.
Document type :
Journal articles
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.inria.fr/hal-00645929
Contributor : Alessandra Bernardi <>
Submitted on : Monday, November 28, 2011 - 7:10:46 PM
Last modification on : Thursday, January 11, 2018 - 4:03:58 PM
Long-term archiving on : Wednesday, February 29, 2012 - 2:31:03 AM

File

SecVar_to_OsculatingVar.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00645929, version 1

Collections

Citation

Alessandra Bernardi, Maria Virgina Catalisano. Some defective secant varieties to osculating varieties of Veronese surfaces. Collectanea Mathematica, Universitat de Barcellona, 2006, 57 (1), pp.43-68. ⟨hal-00645929⟩

Share

Metrics

Record views

432

Files downloads

98