The McKay correspondence, tilting, and rationality

Morgan Brown, Ian Shipman

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the problem of comparing t-structures under the derived McKay correspondence and for tilting equivalences. In low-dimensional cases, we relate the t-structures via torsion theories arising from additive functions on the triangulated category. As an application, we give a criterion for rationality for surfaces with a tilting bundle. We also show that every smooth projective surface that admits a full, strong, and exceptional collection of line bundles is rational.

Original languageEnglish (US)
Pages (from-to)785-811
Number of pages27
JournalMichigan Mathematical Journal
Volume66
Issue number4
DOIs
StatePublished - Nov 1 2017

Fingerprint

McKay Correspondence
T-structure
Tilting
Rationality
Torsion Theory
Triangulated Category
Additive Function
Line Bundle
Bundle
Equivalence

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The McKay correspondence, tilting, and rationality. / Brown, Morgan; Shipman, Ian.

In: Michigan Mathematical Journal, Vol. 66, No. 4, 01.11.2017, p. 785-811.

Research output: Contribution to journalArticle

Brown, Morgan ; Shipman, Ian. / The McKay correspondence, tilting, and rationality. In: Michigan Mathematical Journal. 2017 ; Vol. 66, No. 4. pp. 785-811.
@article{9dfcd0c7eb5340f791c9e7592f039aa2,
title = "The McKay correspondence, tilting, and rationality",
abstract = "We consider the problem of comparing t-structures under the derived McKay correspondence and for tilting equivalences. In low-dimensional cases, we relate the t-structures via torsion theories arising from additive functions on the triangulated category. As an application, we give a criterion for rationality for surfaces with a tilting bundle. We also show that every smooth projective surface that admits a full, strong, and exceptional collection of line bundles is rational.",
author = "Morgan Brown and Ian Shipman",
year = "2017",
month = "11",
day = "1",
doi = "10.1307/mmj/1501034511",
language = "English (US)",
volume = "66",
pages = "785--811",
journal = "Michigan Mathematical Journal",
issn = "0026-2285",
publisher = "University of Michigan",
number = "4",

}

TY - JOUR

T1 - The McKay correspondence, tilting, and rationality

AU - Brown, Morgan

AU - Shipman, Ian

PY - 2017/11/1

Y1 - 2017/11/1

N2 - We consider the problem of comparing t-structures under the derived McKay correspondence and for tilting equivalences. In low-dimensional cases, we relate the t-structures via torsion theories arising from additive functions on the triangulated category. As an application, we give a criterion for rationality for surfaces with a tilting bundle. We also show that every smooth projective surface that admits a full, strong, and exceptional collection of line bundles is rational.

AB - We consider the problem of comparing t-structures under the derived McKay correspondence and for tilting equivalences. In low-dimensional cases, we relate the t-structures via torsion theories arising from additive functions on the triangulated category. As an application, we give a criterion for rationality for surfaces with a tilting bundle. We also show that every smooth projective surface that admits a full, strong, and exceptional collection of line bundles is rational.

UR - http://www.scopus.com/inward/record.url?scp=85034225242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034225242&partnerID=8YFLogxK

U2 - 10.1307/mmj/1501034511

DO - 10.1307/mmj/1501034511

M3 - Article

AN - SCOPUS:85034225242

VL - 66

SP - 785

EP - 811

JO - Michigan Mathematical Journal

JF - Michigan Mathematical Journal

SN - 0026-2285

IS - 4

ER -