[La (co)homologie des espaces de moduli de Deligne–Mumford de courbes rationnelles marquées]
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.
Révisé le :
Accepté le :
Publié le :
Aleksey Zinger 1

@article{CRMATH_2025__363_G4_429_0, author = {Aleksey Zinger}, title = {The (co)homology of the {Deligne{\textendash}Mumford} moduli spaces of marked rational curves}, journal = {Comptes Rendus. Math\'ematique}, pages = {429--436}, publisher = {Acad\'emie des sciences, Paris}, volume = {363}, year = {2025}, doi = {10.5802/crmath.733}, language = {en}, }
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] The cohomology ring of the Deligne–Mumford moduli space of real rational curves with conjugate marked points (2024) | arXiv
[2] Blowdowns of the Deligne–Mumford spaces of real rational curves (2024) | arXiv
[3] 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] Enumeration of real curves in
[5] Algebraic properties of real Gromov–Witten invariants, J. Math. Phys., Volume 66 (2025) no. 1, 012302, 30 pages | DOI | MR | Zbl
[6] 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] Colored operads, series on colored operads, and combinatorial generating systems, Discrete Math., Volume 342 (2019) no. 6, pp. 1624-1657 | DOI | MR | Zbl
[8] Intersection theory of moduli space of stable
[9] Real algebraic maximal varieties, Mat. Zametki, Volume 73 (2003) no. 6, pp. 853-860 | DOI | MR
[10] The homology of real subspace arrangements, J. Topol., Volume 3 (2010) no. 4, pp. 786-818 | DOI | MR | Zbl
[11] Smooth blowups: global vs. local perspectives (2024) | arXiv
Cité par Sources :
Commentaires - Politique