Tilting generators via ample line bundles

Toda, Yukinobu; Uehara, Hokuto

doi:10.1016/j.aim.2009.07.006

Cited by 34 publications

(36 citation statements)

References 16 publications

(34 reference statements)

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“…Now p is affine hence p * is injective, and T P is the Beilinson tilting generator for PV (see [27,Example 7]). We deduce that T ⊥ 0 0 and this completes the proof.…”

Section: A Tilting Generator For Xmentioning

confidence: 99%

“…Definition B.2 (cf. [27,Definition 6]). We say that a locally free sheaf E on a scheme X, where X is projective over a Noetherian affine of finite type, is a tilting generator for…”

Section: B1 Definitionsmentioning

confidence: 99%

“…We show how to deduce the second from Proposition B.4. Following [27,Lemma 8], we consider the canonical map…”

Section: B2 Boundedness For Tilting Functorsmentioning

confidence: 99%

“…(We reuse the notation p for the projection T ∨ Gr → Gr.) For a construction of a tilting generator on T ∨ Gr(2, 4) by another method, see [27].…”

Section: Proof Consideringmentioning

confidence: 99%

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Grassmannian twists on the derived category via spherical functors

Donovan

2013

Proceedings of the London Mathematical Society

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We construct new examples of derived autoequivalences for a family of higher‐dimensional Calabi–Yau varieties. Specifically, we take the total spaces of certain natural vector bundles over Grassmannians double-struckGdouble-struckr(r,d) of r‐planes in a d‐dimensional vector space, and define endofunctors of the bounded derived categories of coherent sheaves associated to these varieties. In the case r = 2, we show that these are autoequivalences using the theory of spherical functors. Our autoequivalences naturally generalize the Seidel–Thomas spherical twist for analogous bundles over projective spaces.

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“…Now p is affine hence p * is injective, and T P is the Beilinson tilting generator for PV (see [27,Example 7]). We deduce that T ⊥ 0 0 and this completes the proof.…”

Section: A Tilting Generator For Xmentioning

confidence: 99%

“…Definition B.2 (cf. [27,Definition 6]). We say that a locally free sheaf E on a scheme X, where X is projective over a Noetherian affine of finite type, is a tilting generator for…”

Section: B1 Definitionsmentioning

confidence: 99%

“…We show how to deduce the second from Proposition B.4. Following [27,Lemma 8], we consider the canonical map…”

Section: B2 Boundedness For Tilting Functorsmentioning

confidence: 99%

“…(We reuse the notation p for the projection T ∨ Gr → Gr.) For a construction of a tilting generator on T ∨ Gr(2, 4) by another method, see [27].…”

Section: Proof Consideringmentioning

confidence: 99%

See 2 more Smart Citations

Grassmannian twists on the derived category via spherical functors

Donovan

2013

Proceedings of the London Mathematical Society

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“…[Bei,Boc2,Bro,Dav,IU,MR]). For more results and examples of NCCRs, we refer to [BLVdB,BIKR,Dao,DFI,DH,IW1,IW3,TU,Wem]. See also a survey article [Leu], and the references therein.…”

Section: Introductionmentioning

confidence: 99%