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The (co)homology of the Deligne–Mumford moduli spaces of marked rational curves
[La (co)homologie des espaces de moduli de Deligne–Mumford de courbes rationnelles marquées]
Comptes Rendus. Mathématique, Volume 363 (2025), pp. 429-436.

This informal note collects key results and open problems on the (co)homology of the Deligne–Mumford moduli spaces of real marked rational curves. The open problems are both of topological nature, aiming to investigate the (co)homology of these spaces further, and of algebraic nature, aiming to describe the structure of the homology of these spaces in operad-like terms.

Cette note informelle rassemble des résultats clés et des problèmes ouverts sur la (co)homologie des espaces de moduli de Deligne–Mumford des courbes rationnelles marquées réelles. Les problèmes ouverts sont à la fois de nature topologique, visant à approfondir l’étude de la (co)homologie de ces espaces, et de nature algébrique, visant à décrire la structure de l’homologie de ces espaces en termes d’opérades.

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DOI : 10.5802/crmath.733

Aleksey Zinger 1

1 Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, United States of America
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Aleksey Zinger. The (co)homology of the Deligne–Mumford moduli spaces of marked rational curves. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 429-436. doi : 10.5802/crmath.733. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.733/

[1] Xujia Chen; Penka Georgieva; Aleksey Zinger The cohomology ring of the Deligne–Mumford moduli space of real rational curves with conjugate marked points (2024) | arXiv

[2] Xujia Chen; Aleksey Zinger Blowdowns of the Deligne–Mumford spaces of real rational curves (2024) | arXiv

[3] Pavel Etingof; André Henriques; Joel Kamnitzer; Eric M. Rains The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points, Ann. Math. (2), Volume 171 (2010) no. 2, pp. 731-777 | DOI | MR | Zbl

[4] Penka Georgieva; Aleksey Zinger Enumeration of real curves in ℂℙ2n-1 and a Witten–Dijkgraaf–Verlinde–Verlinde relation for real Gromov–Witten invariants, Duke Math. J., Volume 166 (2017) no. 17, pp. 3291-3347 | DOI | MR | Zbl

[5] Penka Georgieva; Aleksey Zinger Algebraic properties of real Gromov–Witten invariants, J. Math. Phys., Volume 66 (2025) no. 1, 012302, 30 pages | DOI | MR | Zbl

[6] Ezra Getzler Operads and moduli spaces of genus 0 Riemann surfaces, The moduli space of curves (Texel Island, 1994) (Progress in Mathematics), Volume 129, Birkhäuser, 1995, pp. 199-230 | DOI | MR | Zbl

[7] Samuele Giraudo Colored operads, series on colored operads, and combinatorial generating systems, Discrete Math., Volume 342 (2019) no. 6, pp. 1624-1657 | DOI | MR | Zbl

[8] Sean Keel Intersection theory of moduli space of stable n-pointed curves of genus zero, Trans. Am. Math. Soc., Volume 330 (1992) no. 2, pp. 545-574 | DOI | MR | Zbl

[9] Vyacheslav Alekseevich Krasnov Real algebraic maximal varieties, Mat. Zametki, Volume 73 (2003) no. 6, pp. 853-860 | DOI | MR

[10] Eric M. Rains The homology of real subspace arrangements, J. Topol., Volume 3 (2010) no. 4, pp. 786-818 | DOI | MR | Zbl

[11] Aleksey Zinger Smooth blowups: global vs. local perspectives (2024) | arXiv

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