Details
| Original language | English |
|---|---|
| Pages (from-to) | 509-548 |
| Number of pages | 40 |
| Journal | Quarterly Journal of Mathematics |
| Volume | 69 |
| Issue number | 2 |
| Early online date | 29 Nov 2017 |
| Publication status | Published - 1 Jun 2018 |
| Externally published | Yes |
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.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Quarterly Journal of Mathematics, Vol. 69, No. 2, 01.06.2018, p. 509-548.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Derived categories of resolutions of cyclic quotient singularities
AU - Krug, Andreas
AU - Ploog, David
AU - Sosna, Pawel
PY - 2018/6/1
Y1 - 2018/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85045988907&partnerID=8YFLogxK
U2 - 10.1093/qmath/hax048
DO - 10.1093/qmath/hax048
M3 - Article
AN - SCOPUS:85045988907
VL - 69
SP - 509
EP - 548
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
IS - 2
ER -