scholarly journals On entropy of spherical twists

2019 ◽  
Vol 148 (3) ◽  
pp. 1003-1014 ◽  
Author(s):  
Genki Ouchi
Keyword(s):  
Spherical Twists

scholarly journals Window shifts, flop equivalences and Grassmannian twists

2014 ◽  
Vol 150 (6) ◽  
pp. 942-978 ◽  
Author(s):  
Will Donovan ◽  
Ed Segal
Keyword(s):  
Vector Bundles ◽  
Derived Categories ◽  
Geometric Construction ◽  
Algebraic Construction ◽  
New Class ◽  
Spherical Twists

AbstractWe introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel–Thomas spherical twists, which can be seen as arising from standard flops. We first give a simple algebraic construction, which is well suited to explicit computations. We then give a geometric construction using spherical functors which we prove is equivalent.

scholarly journals Mukai flops and ℙ-twists

2019 ◽  
Vol 2019 (748) ◽  
pp. 227-240
Author(s):  
Nicolas Addington ◽  
Will Donovan ◽  
Ciaran Meachan
Keyword(s):  
Higher Dimensions ◽  
The Other ◽  
Complete Picture ◽  
Derived Equivalences ◽  
Other Hand ◽  
Spherical Twists ◽  
The One ◽  
The Relationship

Abstract Associated to a Mukai flop {X\dashrightarrow X^{\prime}} is on the one hand a sequence of equivalences {D^{b}(X)\to D^{b}(X^{\prime})} , due to Kawamata and Namikawa, and on the other hand a sequence of autoequivalences of {D^{b}(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.

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