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Mathematics > Algebraic Geometry

arXiv:2203.01031 (math)
[Submitted on 2 Mar 2022 (v1), last revised 12 Dec 2022 (this version, v2)]

Title:Residual categories of quadric surface bundles

Authors:Fei Xie
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Abstract:We show that the residual categories of quadric surface bundles are equivalent to the (twisted) derived categories of some scheme under the following hypotheses. Case 1: The quadric surface bundle has a smooth section. Case 2: The total space of the quadric surface bundle is smooth and the base is a smooth surface. We provide two proofs in Case 1 describing the scheme as the hyperbolic reduction and as a subscheme of the relative Hilbert scheme of lines, respectively. In Case 2, the twisted scheme is obtained by performing birational transformations to the relative Hilbert scheme of lines. Finally, we apply the results to certain complete intersections of quadrics.
Comments: 29 pages; v2: revision per suggestions of the referee, to appear in J. Reine Angew. Math. (Crelle)
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:2203.01031 [math.AG]
  (or arXiv:2203.01031v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2203.01031
Related DOI: https://doi.org/10.1515/crelle-2022-0092

Submission history

From: Fei Xie [view email]
[v1] Wed, 2 Mar 2022 11:10:19 UTC (30 KB)
[v2] Mon, 12 Dec 2022 11:21:14 UTC (34 KB)
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