Derived categories of nodal del Pezzo threefolds

Publikation: Arbeitspapier/Preprint › Preprint

Autoren

  • Nebojsa Pavic
  • Evgeny Shinder

Organisationseinheiten

Externe Organisationen

  • The University of Sheffield
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 10 Aug. 2021

Abstract

We give a complete answer for the existence of Kawamata type semiorthogonal decompositions of derived categories of nodal del Pezzo threefolds. More precisely, we show that nodal non smooth \(V_d\) with \(1\leq d \leq 4\) have no Kawamata type decomposition and that all nodal \(V_5\) admit a Kawamata decomposition. For the proof we go through the classification of singular del Pezzo threefolds, compute divisor class groups of nodal del Pezzo threefolds of small degree and use projection from a line to construct Kawamata semiorthogonal decompositions for \(d = 5\). In the \(V_6\) case such a decomposition has been previously constructed by Kawamata.

Zitieren

Derived categories of nodal del Pezzo threefolds. / Pavic, Nebojsa; Shinder, Evgeny.
2021.

Publikation: Arbeitspapier/Preprint › Preprint

Pavic, N., & Shinder, E. (2021). Derived categories of nodal del Pezzo threefolds. Vorabveröffentlichung online. https://arxiv.org/abs/2108.04499
Pavic N, Shinder E. Derived categories of nodal del Pezzo threefolds. 2021 Aug 10. Epub 2021 Aug 10.
Pavic, Nebojsa ; Shinder, Evgeny. / Derived categories of nodal del Pezzo threefolds. 2021.
Download
@techreport{9783c9f8c1c44f24b43b938f675b9b3d,
title = "Derived categories of nodal del Pezzo threefolds",
abstract = "We give a complete answer for the existence of Kawamata type semiorthogonal decompositions of derived categories of nodal del Pezzo threefolds. More precisely, we show that nodal non smooth \(V_d\) with \(1\leq d \leq 4\) have no Kawamata type decomposition and that all nodal \(V_5\) admit a Kawamata decomposition. For the proof we go through the classification of singular del Pezzo threefolds, compute divisor class groups of nodal del Pezzo threefolds of small degree and use projection from a line to construct Kawamata semiorthogonal decompositions for \(d = 5\). In the \(V_6\) case such a decomposition has been previously constructed by Kawamata. ",
author = "Nebojsa Pavic and Evgeny Shinder",
year = "2021",
month = aug,
day = "10",
language = "English",
type = "WorkingPaper",

}

Download

TY - UNPB

T1 - Derived categories of nodal del Pezzo threefolds

AU - Pavic, Nebojsa

AU - Shinder, Evgeny

PY - 2021/8/10

Y1 - 2021/8/10

N2 - We give a complete answer for the existence of Kawamata type semiorthogonal decompositions of derived categories of nodal del Pezzo threefolds. More precisely, we show that nodal non smooth \(V_d\) with \(1\leq d \leq 4\) have no Kawamata type decomposition and that all nodal \(V_5\) admit a Kawamata decomposition. For the proof we go through the classification of singular del Pezzo threefolds, compute divisor class groups of nodal del Pezzo threefolds of small degree and use projection from a line to construct Kawamata semiorthogonal decompositions for \(d = 5\). In the \(V_6\) case such a decomposition has been previously constructed by Kawamata.

AB - We give a complete answer for the existence of Kawamata type semiorthogonal decompositions of derived categories of nodal del Pezzo threefolds. More precisely, we show that nodal non smooth \(V_d\) with \(1\leq d \leq 4\) have no Kawamata type decomposition and that all nodal \(V_5\) admit a Kawamata decomposition. For the proof we go through the classification of singular del Pezzo threefolds, compute divisor class groups of nodal del Pezzo threefolds of small degree and use projection from a line to construct Kawamata semiorthogonal decompositions for \(d = 5\). In the \(V_6\) case such a decomposition has been previously constructed by Kawamata.

M3 - Preprint

BT - Derived categories of nodal del Pezzo threefolds

ER -