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Ample bodies and Terracini loci of projective varieties

Antonio Laface, Alex Massarenti

Abstract

We introduce the notion of ample body of a projective variety and use it to prove emptiness results for Terracini loci and specific identifiability results for toric and homogeneous varieties.

Ample bodies and Terracini loci of projective varieties

Abstract

We introduce the notion of ample body of a projective variety and use it to prove emptiness results for Terracini loci and specific identifiability results for toric and homogeneous varieties.
Paper Structure (5 sections, 23 theorems, 29 equations)

This paper contains 5 sections, 23 theorems, 29 equations.

Table of Contents

  1. Introduction
  2. Terracini loci, specific identifiability and Bronowski's conjecture
  3. Ample bodies and toric varieties
  4. Applications
  5. Fano varieties

Key Result

Theorem 1.1

Let $P\subseteq M_{\mathbb Q}$ be a full dimensional lattice polytope such that the corresponding projective toric variety $X_P\subseteq\mathbb P^{|P\cap M|-1}$, embedded by a complete linear system $|L|$, is smooth, and set For $2$-Terracini loci the following are equivalent: Furthermore, if $A_{X_P}$ is a normal lattice polytope then the following are equivalent:

Theorems & Definitions (56)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Definition 2.1
  • Remark 2.2
  • Definition 2.3
  • Definition 2.4
  • Proposition 2.5
  • proof
  • Corollary 2.6
  • ...and 46 more