NGUYEN, Duc-Manh

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

NGUYEN, Duc-Manh
Institut de Mathématiques de Bordeaux [IMB]

Idioma

Article de revue

Este ítem está publicado en

Geometry and Topology. 2023

Mathematical Sciences Publishers

Fecha de defensa

2023

Resumen en inglés

Given $d\in \mathbb{N}$, $g\in \mathbb{N} \cup\{0\}$, and an integral vector $\kappa=(k_1,\dots,k_n)$ such that $k_i>-d$ and $k_1+\dots+k_n=d(2g-2)$, let $\Omega^d\mathcal{M}_{g,n}(\kappa)$ denote the moduli space of meromorphic $d$-differentials on Riemann surfaces of genus $g$ whose zeros and poles have orders prescribed by $\kappa$. We show that $\Omega^d\mathcal{M}_{g,n}(\kappa)$ carries a canonical volume form that is parallel with respect to its affine complex manifold structure, and that the total volume of $\mathbb{P}\Omega^d\mathcal{M}_{g,n}(\kappa)=\Omega^d\mathcal{M}_{g,n}/\mathbb{C}^*$ with respect to the measure induced by this volume form is finite.< Leer menos

Metadatos

Compartir este ítem

Licencia de uso del documento

Volume forms on moduli spaces of d-differentials

Idioma

Este ítem está publicado en

Fecha de defensa

Resumen en inglés

URI

Orígen

Centros de investigación