Discriminant Circle Bundles over Local Models of Strebel Graphs and Boutroux Curves
| Autor: | Marco Bertola, D. Korotkin |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Circle bundle FOS: Physical sciences Riemann sphere Dynamical Systems (math.DS) 01 natural sciences Mathematics - Algebraic Geometry Mathematics - Geometric Topology symbols.namesake Quadratic equation 0103 physical sciences FOS: Mathematics Ramanujan tau function Mathematics - Dynamical Systems 0101 mathematics Settore MAT/07 - Fisica Matematica Algebraic Geometry (math.AG) Quadratic differential Mathematical Physics Meromorphic function Mathematics Nonlinear Sciences - Exactly Solvable and Integrable Systems 010102 general mathematics Geometric Topology (math.GT) Statistical and Nonlinear Physics Moduli space Differential Geometry (math.DG) Discriminant symbols 010307 mathematical physics Exactly Solvable and Integrable Systems (nlin.SI) |
| Zdroj: | Theoretical and Mathematical Physics. 197:1535-1571 |
| ISSN: | 1573-9333 0040-5779 |
| DOI: | 10.1134/s0040577918110016 |
| Popis: | We study special circle bundles over two elementary moduli spaces of meromorphic quadratic differentials with real periods denoted by $\mathcal Q_0^{\mathbb R}(-7)$ and $\mathcal Q^{\mathbb R}_0([-3]^2)$. The space $\mathcal Q_0^{\mathbb R}(-7)$ is the moduli space of meromorphic quadratic differentials on the Riemann sphere with one pole of order 7 with real periods; it appears naturally in the study of a neighbourhood of the Witten's cycle $W_1$ in the combinatorial model based on Jenkins-Strebel quadratic differentials of $\mathcal M_{g,n}$. The space $\mathcal Q^{\mathbb R}_0([-3]^2)$ is the moduli space of meromorphic quadratic differentials on the Riemann sphere with two poles of order at most 3 with real periods; it appears in description of a neighbourhood of Kontsevich's boundary $W_{-1,-1}$ of the combinatorial model. The application of the formalism of the Bergman tau-function to the combinatorial model (with the goal of computing analytically Poincare dual cycles to certain combinations of tautological classes) requires the study of special sections of circle bundles over $\mathcal Q_0^{\mathbb R}(-7)$ and $\mathcal Q^{\mathbb R}_0([-3]^2)$; in the case of the space $\mathcal Q_0^{\mathbb R}(-7)$ a section of this circle bundle is given by the argument of the modular discriminant. We study the spaces $\mathcal Q_0^{\mathbb R}(-7)$ and $\mathcal Q^{\mathbb R}_0([-3]^2)$, also called the spaces of Boutroux curves, in detail, together with corresponding circle bundles. Comment: 34 pages, 17 figures; minor linguistic/aesthetic improvements |
| Databáze: | OpenAIRE |
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