Relations among Ρ-Twists

Publikation: Arbeitspapier/Preprint › Preprint

Autoren

  • Andreas Hochenegger
  • Andreas Krug

Organisationseinheiten

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 28 Juli 2022

Abstract

Given two \(\mathbb{P}\)-objects in some algebraic triangulated category, we investigate the possible relations among the associated \(\mathbb{P}\)-twists. The main result is that, under certain technical assumptions, the \(\mathbb{P}\)-twists commute if and only if the \(\mathbb{P}\)-objects are orthogonal. Otherwise, there are no relations at all. In particular, this applies to most of the known pairs of \(\mathbb{P}\)-objects on hyperk\"ahler varieties. In order to show this, we relate \(\mathbb{P}\)-twists to spherical twists and apply known results about the absence of relations between pairs of spherical twists.

Zitieren

Relations among Ρ-Twists. / Hochenegger, Andreas; Krug, Andreas.
2022.

Publikation: Arbeitspapier/Preprint › Preprint

Hochenegger, A., & Krug, A. (2022). Relations among Ρ-Twists. Vorabveröffentlichung online. https://doi.org/10.48550/arXiv.2207.14120
Hochenegger A, Krug A. Relations among Ρ-Twists. 2022 Jul 28. Epub 2022 Jul 28. doi: 10.48550/arXiv.2207.14120
Hochenegger, Andreas ; Krug, Andreas. / Relations among Ρ-Twists. 2022.
Download
@techreport{da462bae2d994550bc9ffc4b18189327,
title = "Relations among Ρ-Twists",
abstract = " Given two \(\mathbb{P}\)-objects in some algebraic triangulated category, we investigate the possible relations among the associated \(\mathbb{P}\)-twists. The main result is that, under certain technical assumptions, the \(\mathbb{P}\)-twists commute if and only if the \(\mathbb{P}\)-objects are orthogonal. Otherwise, there are no relations at all. In particular, this applies to most of the known pairs of \(\mathbb{P}\)-objects on hyperk\{"}ahler varieties. In order to show this, we relate \(\mathbb{P}\)-twists to spherical twists and apply known results about the absence of relations between pairs of spherical twists. ",
keywords = "math.AG, math.CT",
author = "Andreas Hochenegger and Andreas Krug",
note = "19 pages, added references, minor improvements",
year = "2022",
month = jul,
day = "28",
doi = "10.48550/arXiv.2207.14120",
language = "English",
type = "WorkingPaper",

}

Download

TY - UNPB

T1 - Relations among Ρ-Twists

AU - Hochenegger, Andreas

AU - Krug, Andreas

N1 - 19 pages, added references, minor improvements

PY - 2022/7/28

Y1 - 2022/7/28

N2 - Given two \(\mathbb{P}\)-objects in some algebraic triangulated category, we investigate the possible relations among the associated \(\mathbb{P}\)-twists. The main result is that, under certain technical assumptions, the \(\mathbb{P}\)-twists commute if and only if the \(\mathbb{P}\)-objects are orthogonal. Otherwise, there are no relations at all. In particular, this applies to most of the known pairs of \(\mathbb{P}\)-objects on hyperk\"ahler varieties. In order to show this, we relate \(\mathbb{P}\)-twists to spherical twists and apply known results about the absence of relations between pairs of spherical twists.

AB - Given two \(\mathbb{P}\)-objects in some algebraic triangulated category, we investigate the possible relations among the associated \(\mathbb{P}\)-twists. The main result is that, under certain technical assumptions, the \(\mathbb{P}\)-twists commute if and only if the \(\mathbb{P}\)-objects are orthogonal. Otherwise, there are no relations at all. In particular, this applies to most of the known pairs of \(\mathbb{P}\)-objects on hyperk\"ahler varieties. In order to show this, we relate \(\mathbb{P}\)-twists to spherical twists and apply known results about the absence of relations between pairs of spherical twists.

KW - math.AG

KW - math.CT

U2 - 10.48550/arXiv.2207.14120

DO - 10.48550/arXiv.2207.14120

M3 - Preprint

BT - Relations among Ρ-Twists

ER -