Mukai flops and P-twists

X' is on the one hand a sequence of equivalences D(X) -> D(X'), due to Kawamata and Namikawa, and on the other hand a sequence of autoequivalences of D(X), due to Huybrechts and Thomas. We work out a complete picture of the relationship between the two. We do the same for standard flops, relating Bondal and Orlov's derived equivalences to spherical twists, extending a well-known story for the Atiyah flop to higher dimensions.
Comment: 26 pages. Minor changes following referee's suggestions. This is an expanded version of the paper to appear in Crelle -->
Druh dokumentu: Working Paper
DOI: 10.1515/crelle-2016-0024
Přístupová URL adresa: http://arxiv.org/abs/1507.02595
Přírůstkové číslo: edsarx.1507.02595
Autor: Addington, N., Donovan, W., Meachan, C.
Rok vydání: 2015
Předmět:
Zdroj: J. reine angew. Math. 748:227-240, 2019
Druh dokumentu: Working Paper
DOI: 10.1515/crelle-2016-0024
Popis: Associated to a Mukai flop X ---> X' is on the one hand a sequence of equivalences D(X) -> D(X'), due to Kawamata and Namikawa, and on the other hand a sequence of autoequivalences of D(X), due to Huybrechts and Thomas. We work out a complete picture of the relationship between the two. We do the same for standard flops, relating Bondal and Orlov's derived equivalences to spherical twists, extending a well-known story for the Atiyah flop to higher dimensions.
Comment: 26 pages. Minor changes following referee's suggestions. This is an expanded version of the paper to appear in Crelle
Databáze: arXiv
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