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On partially ample Ulrich bundles

Angelo Felice Lopez, Debaditya Raychaudhury

Abstract

We characterize $q$-ample Ulrich bundles on a variety $X \subseteq \mathbb P^N$ with respect to $(q+1)$-dimensional linear spaces contained in $X$.

On partially ample Ulrich bundles

Abstract

We characterize -ample Ulrich bundles on a variety with respect to -dimensional linear spaces contained in .
Paper Structure (6 sections, 5 theorems, 10 equations)

This paper contains 6 sections, 5 theorems, 10 equations.

Table of Contents

  1. Introduction
  2. Notation
  3. Generalities on vector bundles
  4. $q$-ample vector bundles
  5. Proofs of the main results
  6. Augmented base loci of Ulrich bundles

Key Result

Theorem 1

Let $X \subset \mathbb{P}^N$ be a smooth variety of dimension $n \ge 1$. Let $\mathcal{E}$ be an Ulrich vector bundle and let $q \ge 0$ be an integer. Then the following are equivalent:

Theorems & Definitions (15)

  • Definition 1.1
  • Theorem 1
  • Corollary 1
  • Definition 3.1
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Definition 4.1
  • Remark 4.2
  • ...and 5 more