Secant varieties to osculating varieties of Veronese embeddings of P^n
| Autor: | Alessandra Bernardi, Alessandro Gimigliano, Maria Virginia Catalisano, Monica Idà |
|---|---|
| Přispěvatelé: | Geometry, algebra, algorithms (GALAAD), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Ingegneria della produzione, termoenergetica e modelli matematici (DIPTEM), Università degli studi di Genova = University of Genoa (UniGe), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), European Project: 252367,EC:FP7:PEOPLE,FP7-PEOPLE-2009-IEF,DECONSTRUCT(2010), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (... - 2019) (UNS), Universita degli studi di Genova, A.Bernardi, M.V.Catalisano, A.Gimigliano, M.Idà. |
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Hilbert series and Hilbert polynomial
Algebra and Number Theory Conjecture MAT/03 Geometria Varietà delle Secanti Varietà di Veronese Varietà Osculanti Varietà Tangenziali Lemma d'Horace Differenziale 010102 general mathematics Dimension (graph theory) Sigma 010103 numerical & computational mathematics Algebraic geometry 01 natural sciences Combinatorics symbols.namesake Mathematics::Algebraic Geometry Secant varieties Tensor decomposition symbols Embedding [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 0101 mathematics Variety (universal algebra) Mathematics Osculating circle |
| Zdroj: | Journal of Algebra Journal of Algebra, 2009, 321 (3), pp.982-1004. ⟨10.1016/j.jalgebra.2008.10.020⟩ Journal of Algebra, Elsevier, 2009, 321 (3), pp.982-1004. ⟨10.1016/j.jalgebra.2008.10.020⟩ Bernardi, Alessandra ; Catalisano, Maria Virginia ; Gimigliano, Alessandro ; Idà, Monica (2008) Secant varieties to osculating varieties of Veronese embeddings of $P^n$. [Preprint] |
| ISSN: | 0021-8693 1090-266X |
| DOI: | 10.1016/j.jalgebra.2008.10.020⟩ |
| Popis: | International audience; A well known theorem by Alexander-Hirschowitz states that all the higher secant varieties of $V_{n,d}$ (the $d$-uple embedding of $\PP n$) have the expected dimension, with few known exceptions. We study here the same problem for $T_{n,d}$, the tangential variety to $V_{n,d}$, and prove a conjecture, which is the analogous of Alexander-Hirschowitz theorem, for $n\leq 9$. Moreover. we prove that it holds for any $n,d$ if it holds for $d=3$. Then we generalize to the case of $O_{k,n,d}$, the $k$-osculating variety to $V_{n,d}$, proving, for $n=2$, a conjecture that relates the defectivity of $\sigma_s(O_{k,n,d})$ to the Hilbert function of certain sets of fat points in $\PP n$. |
| Databáze: | OpenAIRE |
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