Moduli stack of curve

Author: ndzi

August undefined, 2024

http://math.stanford.edu/~conrad/papers/kmpaper.pdf Webof the moduli stack BunG,C of all G-bundles on C (section 5.7). Perhaps contrary to …

Good introductory references on moduli (stacks), for arithmetic objects

Webprojective curve. Introduction Let M be the moduli stack of stable curves of genus 2 and write for its corresponding moduli space. We prove that the moduli of stable curves is projective in the following sense, see Theorem 1.7.2: Theorem The Deligne Mumford moduli space of stable curves of genus 2 is a projective scheme over Spec (Z). Web2 aug. 2024 · Lizhen Ji, Shing-Tung Yau, Transformation Groups and Moduli Spaces of Curves, International Press of Boston 2011 (ISBN:9781571462237) Discussion of the orbifold cohomology of the moduli stack is in. John Harer, The cohomology of the moduli space of curves, Lec. Notes in Math. 1337, p. 138–221. Springer, Berlin, 1988. robert assl

arXiv:math/9805101v1 [math.AG] 22 May 1998

WebIn the present talk, we study the multiplication-by-p map on an elliptic curve E, which gives a stratiﬁcation of Mell into ordinary and supersingular loci, and discuss how this enables us to study the height one and two strata of the moduli stack of formal groups. 1. ORDINARY AND SUPERSINGULAR ELLIPTIC CURVES Web27 aug. 2024 · The aim is to provide a brief introduction to algebraic stacks, and then to … WebThe moduli stack M1 is regular and connected with M a dense open substack that we … robert ast md

Lectures on the Moduli Stack of Vector Bundles on a Curve

Fundamental group of the moduli stack of elliptic curves

Web6 okt. 2024 · Summary. In this expository paper, we show that the Deligne–Mumford moduli space of stable curves is projective over Spec (Ζ). The proof we exposit is due to Kollár. Ampleness of a line bundle is deduced from nefness of a related vector bundle via the Ampleness Lemma, a classifying map construction. The main positivity result concerns … Web15 nov. 2024 · 4.2. Line bundles and Picard groups of the moduli stack of stable curves. We will first consider some special line bundles on the moduli stack of stable curves $\overline{\mathscr{M}}_{g,n}$, including Hodge bundle, point bundles and boundary divisors, tangent bundle, cotangent bundle and normal bundle. robert asprin quotesWeb9 dec. 2008 · These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and stacks) important in the study of moduli spaces of curves and abelian varieties through the example of … robert astbury

"WebModuli of marked curves. One can also enrich the problem by considering the moduli … " - Moduli stack of curve

Moduli stack of curve

Web13 apr. 2024 · Profinite complexes of curves, their automorphisms and anabelian properties of moduli stacks of curves 作者: M. Boggi, P. Lochak 来自arXiv 2024-04-13 01:09:27 Web8. Topics in Moduli Theory. Expand all Collapse all. Chapter 107: Moduli Stacks. Section 107.1: Introduction. Section 107.2: Conventions and abuse of language. Section 107.3: Properties of Hom and Isom. Section 107.4: Properties of the stack of coherent sheaves. Section 107.5: Properties of Quot.

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WebIn this chapter we construct the moduli space \overline {M}_ {g,n} of stable n -pointed curves of genus g and look at its structure from various points of view. First we construct \overline {M}_ {g,n} as an analytic space, and then we show that this analytic space has a natural structure of algebraic space. After a utilitarian introduction to ... Webof the moduli stack BunG,C of all G-bundles on C (section 5.7). Perhaps contrary to one’s ﬁrst impression, the stack turns out to be the more accessible of the two objects for this problem. We show that for all i, the variation of mixed Hodge structure associated to Hi(BunG,C) can be built out of the tautological variation

WebMODULI OF CURVES 3 Conversely,letX→Tbeafamilyofcurves.ThenthebasechangeX U determines amorphismw: U→Curves andthecanonicalisomorphismX U× U,sR→X U× U,tR determinesa2-arroww s→w tsatisfyingthecocyclecondition.Thusamorphism v: T = [U/R] →Curves by the universal property of the quotient [U/R], see Groupoids in Spaces, … Web11 apr. 2024 · Tools. In algebraic geometry, Behrend's trace formula is a generalization of the Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field conjectured in 1993 [1] and proven in 2003 [2] by Kai Behrend. Unlike the classical one, the formula counts points in the "stacky way"; it takes into account the presence of ...

WebMODULI STACK OF ELLIPTIC CURVES 3 Lemma2.5. (1)Let p: E!Spec(R) bequasi … WebLecture 23-24: The moduli of curves 1 The functor of genus g curves First try: (g 2 morphisms are automatically projective) Deﬁnition 1. A smooth curve over S is a ﬂat and proper morphism f : X !S with smooth geometrically connected 1-dimensional ﬁbers. The genus of X !S is the genus of a geometric ﬁber.1 p0M g: Sch Z!Set

Smooth Deligne-Mumford stack The moduli stack of elliptic curves is a smooth separated Deligne–Mumford stack of finite type over $${\displaystyle {\text{Spec}}(\mathbb {Z} )}$$, but is not a scheme as elliptic curves have non-trivial automorphisms. j-invariant There is a proper morphism of … Meer weergeven In mathematics, the moduli stack of elliptic curves, denoted as $${\displaystyle {\mathcal {M}}_{1,1}}$$ or $${\displaystyle {\mathcal {M}}_{\textrm {ell}}}$$, is an algebraic stack over Meer weergeven • Fundamental domain • Homothety • Level structure (algebraic geometry) • Moduli of abelian varieties • Shimura variety Meer weergeven It is a classical observation that every elliptic curve over $${\displaystyle \mathbb {C} }$$ is classified by its periods. Given a basis for its integral homology $${\displaystyle \alpha ,\beta \in H_{1}(E,\mathbb {Z} )}$$ and a global holomorphic … Meer weergeven • moduli+stack+of+elliptic+curves at the nLab • "The moduli stack of elliptic curves", Stacks project Meer weergeven

Web0,n of rational n-marked curves, the moduli stack M g,n of n-marked genus g in general does not embed into a toric variety nicely, i.e., we do not have an embedding of M g,n into some toric variety X such that there is natural correspondence between the cycles on M g,n and the cycles in X. Costello shows that intersection numbers of Psi-classes ... robert aston townebankWebNOTES ON THE CONSTRUCTION OF THE MODULI SPACE OF CURVES DAN EDIDIN The purpose of these notes is to discuss the problem of moduli for curves of genus g≥ 31and outline the construction of the (coarse) moduli scheme of stable curves due to Gieseker. We present few com- plete proofs. robert associates real estateWebModuli stack of elliptic curves, Version 0.3, joint with Lennart Meier - here, we collected the argument - well-known to the experts - for the stack property of the moduli stack of elliptic curves. Previous Teaching Winter term 2024/2024, Bochum robert astles