About: Moduli of algebraic curves

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In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem.

Attributes	Values
rdfs:label	Moduli of algebraic curves (en) Модули римановой поверхности (ru)
rdfs:comment	Модули римановой поверхности — численные характеристики (параметры), одни и те же для всех конформно эквивалентных римановых поверхностей, в своей совокупности характеризующие эквивалентности данной римановой поверхности. (ru) In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem. (en)
dct:subject	Algebraic varieties Moduli theory
Wikipage page ID	3010057 (xsd:integer)
Wikipage revision ID	1097275273 (xsd:integer)
Link from a Wikipage to another Wikipage	Princeton University Press Witten conjecture Bernhard Riemann David Mumford Algebraic group Algebraic stack Algebraic varieties Moduli theory Deformation (mathematics) Level structure (algebraic geometry) Weighted projective space Compact space Complex numbers Chow ring Genus (mathematics) Normal scheme Graph (discrete mathematics) Modular form Arithmetic genus Complete variety Deligne–Mumford stack Publications Mathématiques de l'IHÉS GIT quotient Linear system of divisors Riemann–Hurwitz formula Alexander Grothendieck Algebraic curve Algebraic geometry Field (mathematics) Deformation Theory Hilbert scheme Irreducible component J-invariant Hyperelliptic curve Abelian variety Moduli space Moduli stack of elliptic curves Pierre Deligne Grothendieck–Riemann–Roch theorem Kodaira dimension Michael Rapoport Orbifold Scheme (mathematics) Compact Riemann surface Stable curve Glossary of algebraic geometry Tautological ring Smooth morphism Riemann–Roch theorem Proper scheme Springer Verlag Genus degree formula Unirational Stack quotient Hilbert polynomial dbr:Moduli_of_marked_curves
Link from a Wikipage to an external page	https://people.math.ethz.ch/~rahul/tnt.pdf%7Ctitle= http://archive.numdam.org/article/PMIHES_1969__36__75_0.pdf http://archive.numdam.org/article/SHC_1960-1961__13_1_A4_0.pdf http://aimath.org/WWN/modspacecurves/ https://www-fourier.ujf-grenoble.fr/sites/ifmaquette.ujf-grenoble.fr/files/ete2011-zvonkine.pdf%7Cdoi=10.4171/103-1/12%7Cisbn=978-3-03719-103-3%7Cmr=2952773 https://web.archive.org/web/20180123190525/http:/w3.impa.br/~massaren/files/smgwqc.pdf
sameAs	Moduli of algebraic curves Moduli of algebraic curves Moduli of algebraic curves Moduli of algebraic curves
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Main dbt:More_citations_needed dbt:Reflist dbt:Algebraic_curves_navbox
has abstract	In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem. The most basic problem is that of moduli of smooth complete curves of a fixed genus. Over the field of complex numbers these correspond precisely to compact Riemann surfaces of the given genus, for which Bernhard Riemann proved the first results about moduli spaces, in particular their dimensions ("number of parameters on which the complex structure depends"). (en) Модули римановой поверхности — численные характеристики (параметры), одни и те же для всех конформно эквивалентных римановых поверхностей, в своей совокупности характеризующие эквивалентности данной римановой поверхности. (ru)
gold:hypernym	Space
prov:wasDerivedFrom	wikipedia-en:Moduli_of_algebraic_curves?oldid=1097275273&ns=0
page length (characters) of wiki page	23983 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Moduli_of_algebraic_curves
is Link from a Wikipage to another Wikipage of	Eleny Ionel List of algebraic geometry topics Mirror symmetry conjecture Bernhard Riemann Degenerate conic Algebraic stack Deformation (mathematics) ELSV formula Leticia Brambila Paz Essential dimension Wolf Prize in Mathematics Quotient stack Arithmetic geometry Compactification (mathematics)

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