Deligne Products of Line Bundles over Moduli Spaces of Curves

Weng, Lin; Zagier, Don

doi:10.1007/s00220-008-0494-5

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2023

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“…Example 2.1 (Weng-Zagier [WZ08]). Consider the moduli stack S = M g,N of curves of genus g with N ordered marked points P 1 , .…”

Section: Examplesmentioning

confidence: 99%

Fiber integration of gerbes and Deligne line bundles

Aldrovandi¹,

Ramachandran²

2023

Homology, Homotopy and Applications

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Let π : X → S be a family of smooth projective curves, and let L and M be a pair of line bundles on X. We show that Deligne's line bundle ⟨L, M ⟩ can be obtained from the K 2 -gerbe G L,M constructed in [AR16] via an integration along the fiber map for gerbes that categorifies the well known one arising from the Leray spectral sequence of π. Our construction provides a full account of the biadditivity properties of ⟨L, M ⟩. Our main application is to the categorification of correspondences on the self-product of a curve.The functorial description of the low degree maps in the Leray spectral sequence for π that we develop is of independent interest, and, along the way, we provide an example of their application to the Brauer group.

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“…Example 2.1 (Weng-Zagier [WZ08]). Consider the moduli stack S = M g,N of curves of genus g with N ordered marked points P 1 , .…”

Section: Examplesmentioning

confidence: 99%