On the secant varieties of tangential varieties
Edoardo Ballico

TL;DR
This paper computes the dimensions of secant varieties of tangential varieties for Veronese embeddings, establishing non-defectiveness results and providing formulas for specific cases using classical and recent theorems.
Contribution
It extends known results on secant varieties by computing their dimensions for Veronese embeddings and proves non-defectiveness under certain conditions.
Findings
Dimension formulas for secant varieties of tangential varieties of Veronese embeddings.
Non-defectiveness of tangential varieties for certain Segre-Veronese embeddings.
Existence of a threshold for line bundle tensor powers ensuring non-defectiveness.
Abstract
Let be an integral and non-degenerate variety. Let , , be the join of copies of and copies of the tangential variety of . Using the classical Alexander-Hirschowitz theorem (case ) and a recent paper by H. Abo and N. Vannieuwenhoven (case ) we compute in many cases when is the -Veronese embedding of . This is related to certain additive decompositions of homogeneous polynomials. We give a general theorem proving that is the expected one when has a suitable Segre-Veronese style embedding in . As a corollary we prove that if , , and the tangential variety of embedded by $|\mathcal{O} _{(\mathbb{P}…
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Taxonomy
TopicsTensor decomposition and applications · Phytoestrogen effects and research
