moduli space of Riemann surfaces

GPTKB entity

Statements (52)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
moduli space
gptkbp:compact gptkb:Deligne–Mumford_compactification
gptkbp:containsGenus g
gptkbp:dimensions 0 for genus 0
1 for genus 1
3 for genus 2
3g-3 for genus g > 1
6 for genus 3
9 for genus 4
gptkbp:generalizes moduli space of algebraic curves
gptkbp:hasPoint correspond to isomorphism classes of compact Riemann surfaces
https://www.w3.org/2000/01/rdf-schema#label moduli space of Riemann surfaces
gptkbp:importantFor gptkb:string_theory
mathematical physics
gptkbp:isQuotientOf Teichmüller space by mapping class group
gptkbp:namedAfter gptkb:Bernhard_Riemann
gptkbp:notation gptkb:Mg
gptkbp:parameter isomorphism classes of Riemann surfaces
gptkbp:relatedTo gptkb:Hurwitz_spaces
gptkb:Teichmüller_space
gptkb:moduli_space_of_abelian_varieties
gptkb:moduli_problem
modular forms
moduli space
mapping class group
Jacobians
mapping class group action
moduli functor
moduli space of hyperelliptic curves
moduli space of pointed curves
moduli space of stable curves
moduli space of super Riemann surfaces
moduli stack of curves
period mapping
universal curve
universal family of curves
gptkbp:structure gptkb:algebraic_geometry
complex orbifold
gptkbp:studiedBy gptkb:Oswald_Teichmüller
gptkbp:studiedIn gptkb:algebraic_geometry
complex analysis
differential geometry
gptkbp:bfsParent gptkb:mapping_class_group
gptkb:quantum_Teichmüller_theory
gptkb:Weil–Petersson_metric
gptkb:Fenchel–Nielsen_coordinates
gptkb:Teichmüller_space
gptkb:moduli_space_of_curves
gptkb:Teichmüller_mapping
gptkb:Weil–Petersson_volume
gptkbp:bfsLayer 6