Window shifts, flop equivalences and Grassmannian twists

By Will Donovan, E. Segal. Compositio Mathematica, 2012

73 citations recorded by the source corpus.

Abstract We 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.

View Paper: https://www.semanticscholar.org/paper/22a9d2cbf7d74ff84c1457104b566d9ebc9320de

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1. M. Romo
2. K. Hori
3. Nicolas Addington
4. C. Vafa
5. F. Benini
6. I. Brunner
7. Joaquim Gomis
8. David Tong

Citations in the corpus

• The derived category of a GIT quotient (2012, methodology): “For instance, one can recover a result of Segal & Donovan [11]: Example 4.12 (Grassmannian flop).”
• New derived symmetries of some hyperkähler varieties (2011, background): “He and Segal [13] extended this to a sequence of vector bundles Er on Gr(r, d) and spherical functors D b(Er)→ Db(Er+1) in which the twist of each is the cotwist of the next, again up to a shift and a line bundle.”
• Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary (2013, methodology): “We decided to look at this example because this is one of the first examples in a work by Donnovan-Segal [41] which studies aspects of (classical) grade restriction rule in a class of non-Abelian linear sigma models.”