When is the self-intersection of a subvariety a fibration?

Arinkin, Dima; Căldăraru, Andrei

doi:10.1016/j.aim.2012.05.014

Cited by 40 publications

(194 citation statements)

References 20 publications

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“…The proof is essentially the same as the one of the corresponding result in [1], [2]. Therefore we only review the main points of the proof highlighting the aspects that are special to the twisted case.…”

Section: 5mentioning

confidence: 88%

“…In this section we discuss derived intersections in twisted spaces, generalizing the results of [1] and [2]. We argue that there is a natural twisted HKR class with similar properties to those of the usual one.…”

Section: Twisted Derived Intersectionsmentioning

confidence: 99%

“…Independently of the work of Deligne and Illusie the first two authors proved the following result in [1].…”

Section: Introductionmentioning

confidence: 96%

“…while the second isomorphism is the main result of [1], and its existence follows from the fact that i is split to first order. (Throughout this proof we will implicitly assume that all fiber products are derived, dropping the superscript "R" for simplicity.)…”

Section: 5mentioning

confidence: 99%

“…Note that the condition thatī splits to first order means that the splitting π : X (1) → X must satisfy the condition that π * (A | X ) ∼ = A | X (1) . The entire discussion above makes no assumptions on the splitting of A on X or Y.…”

Section: 5mentioning

confidence: 99%

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Derived intersections and the Hodge theorem

Căldăraru¹

2017

Alg. Geom.

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The algebraic Hodge theorem was proved in a beautiful 1987 paper by Deligne and Illusie, using positive characteristic methods. We argue that the central algebraic object of their proof can be understood geometrically as a line bundle on a derived scheme. In this interpretation, the Deligne-Illusie result can be seen as a proof that this line bundle is trivial under certain assumptions.We give a criterion for the triviality of this line bundle in a more general context. The proof uses techniques from derived algebraic geometry, specifically arguments which show the formality of certain derived intersections. Applying our criterion we recover Deligne and Illusie's original result. We also apply these techniques to the result of Barannikov-Kontsevich, Sabbah, and Ogus-Vologodsky concerning the formality of the twisted de Rham complex.

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Section: 5mentioning

confidence: 88%

Section: Twisted Derived Intersectionsmentioning

confidence: 99%

“…Independently of the work of Deligne and Illusie the first two authors proved the following result in [1].…”

Section: Introductionmentioning

confidence: 96%

Section: 5mentioning

confidence: 99%

Section: 5mentioning

confidence: 99%

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Derived intersections and the Hodge theorem

Căldăraru¹

2017

Alg. Geom.

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A Stronger Derived Torelli Theorem for K3 Surfaces

Lieblich

Olsson

2017

Geometry Over Nonclosed Fields

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In an earlier paper the notion of a filtered derived equivalence was introduced, and it was shown that if two K3 surfaces admit such an equivalence then they are isomorphic. In this paper we study more refined aspects of filtered derived equivalences related to the action on the cohomological realizations of the Mukai motive. It is shown that if a filtered derived equivalence between K3 surfaces also preserves ample cones then one can find an isomorphism that induces the same map as the equivalence on the cohomological realizations.

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