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Mathematics > Algebraic Geometry

arXiv:2201.07767 (math)
[Submitted on 19 Jan 2022 (v1), last revised 8 Aug 2022 (this version, v2)]

Title:Second Chern class and Fujiki constants of hyperkähler manifolds

Authors:Thorsten Beckmann, Jieao Song
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Abstract:We study characteristic classes on hyperkähler manifolds with a view towards the Verbitsky component. The case of the second Chern class leads to a conditional upper bound on the second Betti number in terms of the Riemann--Roch polynomial, which is also valid for singular examples. We discuss the general structure of characteristic classes and the Riemann--Roch polynomial on hyperkähler manifolds using among other things Rozansky--Witten theory.
Comments: 25 pages; added an appendix on the singularities of the orbifold K4'
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14J42
Cite as: arXiv:2201.07767 [math.AG]
  (or arXiv:2201.07767v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2201.07767

Submission history

From: Jieao Song [view email]
[v1] Wed, 19 Jan 2022 18:05:13 UTC (28 KB)
[v2] Mon, 8 Aug 2022 14:37:34 UTC (31 KB)
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