Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 567-592 |
| Seitenumfang | 26 |
| Fachzeitschrift | Moscow mathematical journal |
| Jahrgang | 21 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - Juli 2021 |
Abstract
We investigate necessary conditions for Gorenstein projective varieties to admit semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds with isolated compound An singularities. We introduce obstructions coming from Algebraic K-theory and translate them into the concept of maximal nonfactoriality. Using these obstructions we show that many classes of nodal three-folds do not admit Kawamata type semiorthogonal decompositions. These include nodal hypersurfaces and double solids, with the excep-tion of a nodal quadric, and del Pezzo threefolds of degrees 1 ≤ d ≤ 4 with maximal class group rank. We also investigate when does a blow up of a smooth threefold in a singular curve admit a Kawamata type semiorthogonal decomposition and we give a complete answer to this question when the curve is nodal and has only rational components.
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in: Moscow mathematical journal, Jahrgang 21, Nr. 3, 07.2021, S. 567-592.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Obstructions to semiorthogonal decompositions for singular threefolds i
T2 - K-theory
AU - Kalck, Martin
AU - Pavic, Nebojsa
AU - Shinder, Evgeny
N1 - Funding Information: Received November 15, 2019; in revised form June 17, 2020. M.K. was supported in part by the GK1821 at the Universit at Freiburg; the latter grant also allowed for a visit of N.P. to Freiburg. E.S. was supported in part by Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. N 14.641.31.0001.
PY - 2021/7
Y1 - 2021/7
N2 - We investigate necessary conditions for Gorenstein projective varieties to admit semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds with isolated compound An singularities. We introduce obstructions coming from Algebraic K-theory and translate them into the concept of maximal nonfactoriality. Using these obstructions we show that many classes of nodal three-folds do not admit Kawamata type semiorthogonal decompositions. These include nodal hypersurfaces and double solids, with the excep-tion of a nodal quadric, and del Pezzo threefolds of degrees 1 ≤ d ≤ 4 with maximal class group rank. We also investigate when does a blow up of a smooth threefold in a singular curve admit a Kawamata type semiorthogonal decomposition and we give a complete answer to this question when the curve is nodal and has only rational components.
AB - We investigate necessary conditions for Gorenstein projective varieties to admit semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds with isolated compound An singularities. We introduce obstructions coming from Algebraic K-theory and translate them into the concept of maximal nonfactoriality. Using these obstructions we show that many classes of nodal three-folds do not admit Kawamata type semiorthogonal decompositions. These include nodal hypersurfaces and double solids, with the excep-tion of a nodal quadric, and del Pezzo threefolds of degrees 1 ≤ d ≤ 4 with maximal class group rank. We also investigate when does a blow up of a smooth threefold in a singular curve admit a Kawamata type semiorthogonal decomposition and we give a complete answer to this question when the curve is nodal and has only rational components.
KW - Compound A singularities
KW - Derived categories
KW - Kawamata semiorthogonal decompositions
KW - Negative K-theory
KW - Nonfactorial threefolds
UR - http://www.scopus.com/inward/record.url?scp=85109943183&partnerID=8YFLogxK
U2 - 10.17323/1609-4514-2021-21-3-567-592
DO - 10.17323/1609-4514-2021-21-3-567-592
M3 - Article
AN - SCOPUS:85109943183
VL - 21
SP - 567
EP - 592
JO - Moscow mathematical journal
JF - Moscow mathematical journal
SN - 1609-3321
IS - 3
ER -