Geometry of first nonempty Terracini loci
Francesco Galuppi, Pierpaola Santarsiero, Douglas A. Torrance, Ettore, Teixeira Turatti
TL;DR
This paper characterizes the smallest nonempty Terracini loci for specific algebraic varieties, provides a complete description for del Pezzo surfaces, and introduces an algorithm for computing Terracini loci.
Contribution
It offers new characterizations of Terracini loci for Veronese, Segre-Veronese varieties, and del Pezzo surfaces, along with an explicit computational method.
Findings
Smallest nonempty Terracini loci characterized for Veronese and Segre-Veronese varieties.
Complete description of Terracini loci for del Pezzo surfaces.
Algorithm for explicit computation of Terracini loci.
Abstract
After a few results on curves, we characterize the smallest nonempty Terracini loci of Veronese and Segre-Veronese varieties. For del Pezzo surfaces, we give a full description of the Terracini loci. Moreover, we present an algorithm to explicitly compute the Terracini loci of a given variety.
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Taxonomy
TopicsPolynomial and algebraic computation · Tensor decomposition and applications · Advanced Differential Equations and Dynamical Systems