Derived categories of resolutions of cyclic quotient singularities

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Andreas Krug
  • David Ploog
  • Pawel Sosna

Externe Organisationen

  • Philipps-Universität Marburg
  • Freie Universität Berlin (FU Berlin)
  • Universität Hamburg
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Details

OriginalspracheEnglisch
Seiten (von - bis)509-548
Seitenumfang40
FachzeitschriftQuarterly Journal of Mathematics
Jahrgang69
Ausgabenummer2
Frühes Online-Datum29 Nov. 2017
PublikationsstatusVeröffentlicht - 1 Juni 2018
Extern publiziertJa

Abstract

For a cyclic group G acting on a smooth variety X with only one character occurring in the G-equivariant decomposition of the normal bundle of the fixed point locus, we study the derived categories of the orbifold [X/G] and the blow-up resolution Y→X/G. Some results generalize known facts about X=An with diagonal G-action, while other results are new also in this basic case. In particular, if the codimension of the fixed point locus equals |G|, we study the induced tensor products under the equivalence Db(Y)≈Db([X/G]) and give a 'flop-flop = twist' type formula. We also introduce candidates for general constructions of categorical crepant resolutions inside the derived category of a given geometric resolution of singularities and test these candidates on cyclic quotient singularities.

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Derived categories of resolutions of cyclic quotient singularities. / Krug, Andreas; Ploog, David; Sosna, Pawel.
in: Quarterly Journal of Mathematics, Jahrgang 69, Nr. 2, 01.06.2018, S. 509-548.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Krug A, Ploog D, Sosna P. Derived categories of resolutions of cyclic quotient singularities. Quarterly Journal of Mathematics. 2018 Jun 1;69(2):509-548. Epub 2017 Nov 29. doi: 10.1093/qmath/hax048
Krug, Andreas ; Ploog, David ; Sosna, Pawel. / Derived categories of resolutions of cyclic quotient singularities. in: Quarterly Journal of Mathematics. 2018 ; Jahrgang 69, Nr. 2. S. 509-548.
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