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Tr. Mat. Inst. Steklova, 2019, Volume 305, Pages 250–270 (Mi tm3994)  

Compactifications of $\mathcal M_{0,n}$ Associated with Alexander Self-Dual Complexes: Chow Rings, $\psi $-Classes, and Intersection Numbers

Ilia I. Nekrasova, Gaiane Yu. Paninabc

a Chebyshev Laboratory at St. Petersburg State University, 14 liniya Vasil'evskogo ostrova 29B, St. Petersburg, 199178 Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, nab. Fontanki 27, St. Petersburg, Russia
c Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr. 28, Peterhof, St. Petersburg, 198504 Russia

Abstract: An Alexander self-dual complex gives rise to a compactification of $\mathcal M_{0,n}$, 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.

Funding Agency Grant Number
Russian Science Foundation 16-11-10039
This work is supported by the Russian Science Foundation under grant 16-11-10039.


DOI: https://doi.org/10.4213/tm3994

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 305, 232–250

Bibliographic databases:

UDC: 515.165+512.734
Received: September 19, 2018
Revised: December 14, 2018
Accepted: March 2, 2019

Citation: Ilia I. Nekrasov, Gaiane Yu. Panina, “Compactifications of $\mathcal M_{0,n}$ Associated with Alexander Self-Dual Complexes: Chow Rings, $\psi $-Classes, and Intersection Numbers”, Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Tr. Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 250–270; Proc. Steklov Inst. Math., 305 (2019), 232–250

Citation in format AMSBIB
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\by Ilia~I.~Nekrasov, Gaiane~Yu.~Panina
\paper Compactifications of $\mathcal M_{0,n}$ Associated with Alexander Self-Dual Complexes: Chow Rings, $\psi $-Classes, and Intersection Numbers
\inbook Algebraic topology, combinatorics, and mathematical physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 305
\pages 250--270
\publ Steklov Math. Inst. RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3994}
\crossref{https://doi.org/10.4213/tm3994}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 305
\pages 232--250
\crossref{https://doi.org/10.1134/S0081543819030131}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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