An Explicit Derived Equivalence of Azumaya Algebras on K3 Surfaces via Koszul Duality

Ingalls, Colin; Khalid, Madeeha

doi:10.48550/arxiv.1104.4333

Cited by 1 publication

(3 citation statements)

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“…The aim of this section is provide a proof for quadric fibrations with simple degeneration. For quadric surface bundles, this fact has been noted in [69,Lemma 4.2] and [51,Thm. 4.5].…”

Section: Appendix a A Comparison Of Even Clifford Algebrasmentioning

confidence: 56%

“…In particular, projecting T x Q ∩ Q away from x, we find Q ′ as a quadric hypersurface in the target P n−3 , which we call the quadric reduction by hyperbolic splitting associated to Q and x. Recently, this construction was considered [51] in the study of nets of quadrics over P 2 and associated K3 surfaces.…”

Section: Quadratic Forms and Even Clifford Algebrasmentioning

confidence: 99%

“…It would be interesting to give a direct explicit isomorphism between the Severi-Brauer scheme of B 0 and the connected part of the Stein factorization of ΛG(Q). See [51,Thm. 4.5] for an approach in the case of surface bundles.…”

Section: Appendix a A Comparison Of Even Clifford Algebrasmentioning

confidence: 99%

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Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems

Auel

Bernardara

Bolognesi

2014

Journal de Mathématiques Pures et Appliquées

119

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Let X → Y be a fibration whose fibers are complete intersections of r quadrics. We develop new categorical and algebraic tools-a theory of relative homological projective duality and the Morita invariance of the even Clifford algebra under quadric reduction by hyperbolic splitting-to study semiorthogonal decompositions of the bounded derived category D b (X). Together with results in the theory of quadratic forms, we apply these tools in the case where r = 2 and X → Y has relative dimension 1, 2, or 3, in which case the fibers are curves of genus one, Del Pezzo surfaces of degree 4, or Fano threefolds, respectively. In the latter two cases, if Y = P 1 over an algebraically closed field of characteristic zero, we relate rationality questions to categorical representability of X.

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“…The aim of this section is provide a proof for quadric fibrations with simple degeneration. For quadric surface bundles, this fact has been noted in [69,Lemma 4.2] and [51,Thm. 4.5].…”

Section: Appendix a A Comparison Of Even Clifford Algebrasmentioning

confidence: 56%

Section: Quadratic Forms and Even Clifford Algebrasmentioning

confidence: 99%