Moduli spaces for Lamé functions and Abelian differentials of the second kind

DOI10.1142/S0219199721500280zbMath1486.14043arXiv2006.16837MaRDI QIDQ5065097

Andrei Gabrielov, Gabriele Mondello, Alexandre Eremenko, Dmitri Panov

Publication date: 18 March 2022

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.16837

zbMATH Keywords

Lamé equationelliptic curveflat metrictranslation surfaceconic singularityspherical metricAbelian differentialPlane algebraic curve

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Lamé, Mathieu, and spheroidal wave functions (33E10) Families, moduli of curves (analytic) (14H15) Differentials on Riemann surfaces (30F30)

Related Items (2)

Moduli of spherical tori with one conical point ⋮ Classification of generic spherical quadrilaterals

Uses Software

• MathOverflow
• diffstrata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mean field equations, hyperelliptic curves and modular forms. I
• Elliptic functions, Green functions and the mean field equations on tori
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry
• Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory
• Compactification of strata of abelian differentials
• Mean field equations, hyperelliptic curves and modular forms. II
• Spherical surfaces with conical points: systole inequality and moduli spaces with many connected components
• Critical points of the classical Eisenstein series of weight two
• Connected components of the strata of the moduli space of meromorphic differentials
• Green’s function and anti-holomorphic dynamics on a torus
• Extension of embeddings close to isometries or similarities
• Projective structures and projective bundles over compact Riemann surfaces
• Lame equation, sl(2) algebra and isospectral deformations
• Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints
• Metrics of positive curvature with conic singularities on the sphere
• Strata of $k$-differentials
• Group actions, divisors, and plane curves
• Lamé polynomials, hyperelliptic reductions and Lamé band structure

This page was built for publication: Moduli spaces for Lamé functions and Abelian differentials of the second kind