moduli space of Riemann surfaces

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept gptkb: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
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:mapping_class_group gptkb:Hurwitz_spaces gptkb:Teichmüller_space gptkb:moduli_space_of_abelian_varieties gptkb:moduli_problem gptkb:moduli_space modular forms 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:Weil–Petersson_metric gptkb:Fenchel–Nielsen_coordinates
gptkbp:bfsLayer	6
https://www.w3.org/2000/01/rdf-schema#label	moduli space of Riemann surfaces