Abstract
An Alexander self-dual complex gives rise to a compactification of \({{\cal M}_{0,n}}\), called an ASD compactification, which is a smooth algebraic variety. ASD compactifications include (but are not exhausted by) the polygon spaces, or the configuration spaces of flexible polygons. We present an explicit description of the Chow rings of ASD compactifications. We study the analogs of Kontsevich’s tautological bundles, compute their Chern classes, compute top intersections of the Chern classes, and derive a recursion for the intersection numbers.
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This work is supported by the Russian Science Foundation under grant 16-11-10039.
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This article was submitted by the authors simultaneously in Russian and English
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Vol. 305, pp. 250–270.
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Nekrasov, I.I., Panina, G.Y. Compactifications of \({{\cal M}_{0,n}}\) Associated with Alexander Self-Dual Complexes: Chow Rings, ψ-Classes, and Intersection Numbers. Proc. Steklov Inst. Math. 305, 232–250 (2019). https://doi.org/10.1134/S0081543819030131
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DOI: https://doi.org/10.1134/S0081543819030131