# Genus zero modular operad and absolute Galois group

@article{Combe2019GenusZM, title={Genus zero modular operad and absolute Galois group}, author={Noemie C. Combe and Yu. I. Manin}, journal={arXiv: Algebraic Geometry}, year={2019} }

In this article, we develop the geometry of canonical stratifications of the spaces $\overline{\mathcal{M}}_{0,n}$ and prepare ground for studying the action of the Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$ upon strata.

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## References

SHOWING 1-10 OF 59 REFERENCES

Operads and Moduli Spaces of Genus 0 Riemann Surfaces

- Mathematics, Physics
- 1995

In this paper, we study two dg (differential graded) operads related to the homology of moduli spaces of pointed algebraic curves of genus 0. These two operads are dual to each other, in the sense of…

Operads of genus zero curves and the
Grothendieck–Teichmüller group

- MathematicsGeometry & Topology
- 2019

We show that the group of homotopy automorphisms of the profinite completion of the genus zero surface operad is isomorphic to the (profinite) Grothendieck-Teichm\"{u}ller group. Using a result of…

Symmetries of genus zero modular operad

- Mathematics
- 2019

In this article combining survey and certain research results, we introduce a categorical framework for description of symmetries of genus zero modular operad. This description merges the techniques…

Intersection theory of moduli space of stable N-pointed curves of genus zero

- Mathematics
- 1992

We give a new construction of the moduli space via a composition of smooth codimension two blowups and use our construction to determine the Chow ring

Gromov-Witten classes, quantum cohomology, and enumerative geometry

- Physics, Mathematics
- 1994

The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic…

Higher structures, quantum groups and genus zero modular operad

- Mathematics, Computer ScienceJ. Lond. Math. Soc.
- 2019

The interaction of quadratic algebras structure with operadic structure in the context of enriched category formalism due to G. M. Kelly et al. is studied.

Frobenius manifolds, quantum cohomology, and moduli spaces

- Mathematics
- 1999

Introduction: What is quantum cohomology? Introduction to Frobenius manifolds Frobenius manifolds and isomonodromic deformations Frobenius manifolds and moduli spaces of curves Operads, graphs, and…

Hyperplane arrangement cohomology and monomials in the exterior algebra

- Mathematics
- 1999

We show that if X is the complement of a complex hyperplane arrangement, then the homology of X has linear free resolution as a module over the exterior algebra on the first cohomology of X. We study…

Koszul duality for Operads

- Mathematics
- 1994

(0.1) The purpose of this paper is to relate two seemingly disparate developments. One is the theory of graph cohomology of Kontsevich [Kon 2 3] which arose out of earlier works of Penner [Pe] and…

Remarks on the $L^{2}$-cohomology of singular algebraic surfaces

- Mathematics
- 1989

Let X be a normal singular algebraic surface (over C) embedded in the projective space PN(C) and let S be its singularity set, which consists of isolated singular points. By restricting the…