Ample line bundles and generation time-Reference-Cited by-同舟云学术

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Ample line bundles and generation time

Published:2023-06-27 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Olander Noah¹^ORCID

Affiliation:

1. Korteweg-de Vries Institute for Mathematics , University of Amsterdam , Science Park 105-107, 1098 XG Amsterdam , Netherlands

Abstract

AbstractWe prove that ifXis a regular quasi-projective variety of dimensiond, the set of line bundles{𝒪X⁢(n)}n∈ℤ

{\{\mathcal{O}_{X}(n)\}_{n\in{\mathbb{Z}}}}

generates the bounded derived category ofXindsteps. This proves new cases of a conjecture of Orlov as well as a conjecture of Elagin and Lunts.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2023-0036/pdf

Reference14 articles.

1. A. A. Beĭlinson, J. Bernstein and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces. I (Luminy 1981), Astérisque 100, Société Mathématique de France, Paris (1982), 5–171.

2. A. Bondal and M. van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J. 3 (2003), no. 1, 1–36, 258.

3. J. D. Christensen, Ideals in triangulated categories: phantoms, ghosts and skeleta, Adv. Math. 136 (1998), no. 2, 284–339.

4. A. Elagin and V. A. Lunts, Three notions of dimension for triangulated categories, J. Algebra 569 (2021), 334–376.

5. J. C. Letz, Generation time in derived categories, PhD thesis, The University of Utah, 2020.

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