Geodesic
Compactifications of $\mathcal M_{0,n}$ Associated with Alexander Self-Dual Complexes: Chow Rings, $\psi $-Classes, and Intersection Numbers
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 250-270.

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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.
Keywords: Alexander self-dual complex, modular compactification, tautological bundle, Chern class, Chow ring. 
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     author = {Ilia I. Nekrasov and Gaiane Yu. Panina},
     title = {Compactifications of $\mathcal M_{0,n}$ {Associated} with {Alexander} {Self-Dual} {Complexes:} {Chow} {Rings,} $\psi ${-Classes,} and {Intersection} {Numbers}},
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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. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 250-270. http://geodesic.mathdoc.fr/item/TM_2019_305_a12/

[1] Agapito J., Godinho L., “Intersection numbers of polygon spaces”, Trans. Amer. Math. Soc., 361:9 (2009), 4969–4997 | DOI | Zbl

[2] Ceyhan Ö., “Chow groups of the moduli spaces of weighted pointed stable curves of genus zero”, Adv. Math., 221:6 (2009), 1964–1978 | DOI | Zbl

[3] Deligne P., Mumford D., “The irreducibility of the space of curves of given genus”, Publ. math. Inst. hautes étud. sci., 36 (1969), 75–109 | DOI | Zbl

[4] Fulton W., Intersection theory, Springer, Berlin, 1998 | Zbl

[5] Galashin P., Panina G., “Manifolds associated to simple games”, J. Knot Theory Ramifications, 25:12 (2016), 1642003 | DOI | Zbl

[6] Hassett B., “Moduli spaces of weighted pointed stable curves”, Adv. Math., 173:2 (2003), 316–352 | DOI | Zbl

[7] Hausmann J.-C., Knutson A., “The cohomology ring of polygon spaces”, Ann. Inst. Fourier, 48:1 (1998), 281–321 | DOI | Zbl

[8] Keel S., “Intersection theory of moduli space of stable $n$-pointed curves of genus zero”, Trans. Amer. Math. Soc., 330:2 (1992), 545–574 | Zbl

[9] Klyachko A.A., “Spatial polygons and stable configurations of points in the projective line”, Algebraic geometry and its applications, Aspects Math. E, 25, ed. by A. Tikhomirov, A. Tyurin, Vieweg, Braunschweig, 1994, 67–84 | DOI | Zbl

[10] Kontsevich M., “Intersection theory on the moduli space of curves and the matrix Airy function”, Commun. Math. Phys., 147:1 (1992), 1–23 | DOI | Zbl

[11] Losev A., Manin Y., “New moduli spaces of pointed curves and pencils of flat connections”, Mich. Math. J., 48 (2000), 443–472 | DOI | Zbl

[12] Moon H.-B., Summers C., von Albade J., Xie R., “Birational contractions of $\overline {\mathrm M}_{0,n}$ and combinatorics of extremal assignments”, J. Algebr. Comb., 47:1 (2018), 51–90 ; arXiv: 1801.00785 [math.GT] | DOI | Zbl

[13] I. Nekrasov and G. Panina, “Geometric presentation for the cohomology ring of polygon spaces”, Algebra Anal., 31:1 (2019), 80–91 ; E-print, arXiv: 1801.00785 [math.GT]

[14] Von Neumann J., Morgenstern O., Theory of games and economic behavior, Princeton Univ. Press, Princeton, NJ, 1944 | Zbl

[15] Smyth D.I., “Towards a classification of modular compactifications of $\mathcal M_{g,n}$”, Invent. math., 192:2 (2013), 459–503 | DOI | Zbl