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...h>, then ''Y'' is called ''a'' coarse moduli stack of ''X''. ("The" coarse moduli requires a universality.) ...ra 34 (1984), 193–240, Proceedings of the Luminy conference on algebraic K-theory (Luminy, 1983). ...

...a quasi-projective proper moduli scheme carrying a [[symmetric obstruction theory]], then the '''weighted Euler characteristic''' ...Donaldson–Thomas theory]]) or that of [[stable map]]s (the [[Gromov–Witten theory]]). ...

...lliptic curves with automorphisms, necessitating the construction of the [[Moduli stack of elliptic curves]]. | title = Arithmetic moduli of elliptic curves ...

...[[chromatic homotopy theory|chromatic]] approach to the [[stable homotopy theory]], a branch of [[algebraic topology]]. ...ofinite group]] called the '''Morava stabilizer group'''. The [[Lubin–Tate theory]] describes how the strata <math>\mathcal{M}^n_{\text{FG}}</math> fit toget ...

...hness generalise [[modulus of continuity]] and are used in [[approximation theory]] and [[numerical analysis]] to estimate errors of approximation by [[polyn ==Moduli of smoothness== ...

...ure, one can go further and obtain a [[Moduli_space#Fine_moduli_space|fine moduli space]]. .... If this is instead given by a [[GIT quotient]], then it gives the coarse moduli space <math>A_g</math>. ...

...theory]] of [[algebraic curve]]s. Furthermore, it has applications to the theory of [[modular form]]s on [[reductive group|reductive]] [[algebraic groups]]< | mr=2409679 }}</ref> and [[string theory]].<ref>{{Citation ...

...[[Fano varieties]], [[moduli theory]], and non-commutative [[Brill–Noether theory]]. He also found a new counterexample to [[Hilbert's 14th problem]] (the fi *{{Citation| title = An Introduction to Invariants and Moduli ...

...l|last=Knudsen|first=Finn F.|date=1983-12-01|title=The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$|url=https://www.mscand.dk/ * [https://stacks.math.columbia.edu/tag/04UW Deformation theory and algebraic stacks] - overview of Artin's papers and related research ...

...[[algebraic geometry]], especially [[Moduli space#Moduli of vector bundles|Moduli of Vector Bundles]] on curves.<ref>[http://math.tufts.edu/people/facultyTei ...385-400.<ref>[http://projecteuclid.org/euclid.dmj/1077296363 Brill-Noether theory for vector bundles, Duke Math. J. (1991)]</ref> ...

...ons, a level structure is used in the construction of [[moduli space]]s; a moduli space is often constructed as a quotient. The presence of automorphisms pos ...a lattice containing the defining lattice of the variety. From the moduli theory of elliptic curves, all such lattices can be described as the lattice <math ...

...urve]] that is asymptotically stable in the sense of [[geometric invariant theory]]. ...idifies the curves so that there are no infinitesimal automorphisms of the moduli stack constructed later on, and (3) guarantees that the arithmetic genus of ...

..., the '''tautological ring''' is the subring of the [[Chow ring]] of the [[moduli space of curves]] generated by tautological classes. These are classes obta ...thcal{M}}_{g,n}</math> be the moduli stack of [[Moduli of algebraic curves#Moduli of marked curves|stable marked curves]] <math>(C;x_1,\ldots,x_n)</math>, su ...

...ear= 2004|isbn=0-8218-3485-1| mr=2045629|doi=10.1090/coll/052}}</ref> This moduli space is roughly the collection of maps <math>u</math> from a nodal [[Riema ...[Chern class]] of <math>X</math> is negative. Such configurations make the moduli space very singular so a fundamental class cannot be defined in the usual w ...

...number]]s through [[two-dimensional conformal field theory|conformal field theory]]. ...s|Hamiltonian]]s can be described as follows: the [[tangent space]] to the moduli space of ''G''-bundles at the bundle ''F'' is ...

...quantum cohomology|eprint=alg-geom/9608011|pages=6,12,29,31}}</ref> These moduli spaces are smooth [[orbifold]]s whenever the target space is convex. A vari ...paces of stable curves mapping to convex spaces. That is, the [[Kontsevich moduli space]]s <math>\overline{M}_{0,n}(X,\beta)</math> have nice geometric and d ...

...1|pages=97–124 |year=2003 }} using virtual localization in [[Gromov–Witten theory]]. It is named after the factor of <math>\lambda_g</math>, the ''g''th [[Ch [[Category:Moduli theory]] ...

{{string theory}} ...nnections to [[Gromov–Witten invariant]]s of algebraic three-folds and the theory of stable pairs due to [[Rahul Pandharipande]] and Thomas. ...

...://www.math.ubc.ca/~behrend/thesis.pdf The Lefschetz Trace Formula for the Moduli Stack of Principal Bundles.] PhD dissertation.</ref> and proven in 2003 <re ...via Nonabelian Poincare Duality (282y)|date=Spring 2014}}</ref>) See the [[moduli stack of principal bundles]] and references therein for the precise formula ...

...is a conjecture about [[intersection number]]s of stable classes on the [[moduli space of curves]], introduced by [[Edward Witten]] in the paper {{harvs|txt ...ack]] of [[algebraic curve]]s, and the [[Partition function (quantum field theory)|partition function]] for the other is the logarithm of the τ-function of t ...