Some moduli spaces of smooth complete intersections which are quasi-projective

Olivier Benoist

Displaying similar documents to “Some moduli spaces of smooth complete intersections which are quasi-projective”

Limiting configurations for solutions of Hitchin’s equation

Rafe Mazzeo, Jan Swoboda, Hartmut Weiß, Frederik Witt (2012-2014)

Séminaire de théorie spectrale et géométrie

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We review recent work on the compactification of the moduli space of Hitchin’s self-duality equation. We study the degeneration behavior near the ends of this moduli space in a set of generic directions by showing how limiting configurations can be desingularized. Following ideas of Hitchin, we can relate the top boundary stratum of this space of limiting configurations to a Prym variety. A key role is played by the family of rotationally symmetric solutions to the self-duality equation...

Some results on homotopy theory of modules

Zheng-Xu He (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Seguendo le idee presentate nei lavori [1] e [2] si studiano le proprietà dei gruppi di $i$ -omotopia per moduli ed omomorfismi di moduli.

On the motives of moduli of chains and Higgs bundles

Oscar García-Prada, Jochen Heinloth, Alexander Schmitt (2014)

Journal of the European Mathematical Society

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We take another approach to Hitchin’s strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the $n$ -torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space...

Good moduli spaces for Artin stacks

Jarod Alper (2013)

Annales de l’institut Fourier

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We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford’s geometric invariant theory and tame stacks.

The tautological ring of $M_{1, n}^{c t}$

Mehdi Tavakol (2011)

Annales de l’institut Fourier

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We describe the tautological ring of the moduli space of stable $n$ -pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.

Moduli of smoothness of functions and their derivatives

Z. Ditzian, S. Tikhonov (2007)

Studia Mathematica

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Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for $L_{p} (T)$ and $L_{p} [- 1, 1]$ for 0 < p < ∞ using the moduli of smoothness $ω^{r} {(f, t)}_{p}$ and $ω_{φ}^{r} {(f, t)}_{p}$ respectively.

A Proof Via the Seiberg-Witten Moduli Space of Donaldson’s Theorem on Smooth $4$ -Manifolds with Definite Intersection Forms

Mikhail Katz (1995)

Recherche Coopérative sur Programme n°25

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The Kodaira dimension of the moduli space of Prym varieties

Gavril Farkas, Katharina Ludwig (2010)

Journal of the European Mathematical Society

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We study the enumerative geometry of the moduli space $ℛ_{g}$ of Prym varieties of dimension $g - 1$ . Our main result is that the compactication of $ℛ_{g}$ is of general type as soon as $g > 13$ and $g$ is different from 15. We achieve this by computing the class of two types of cycles on $ℛ_{g}$ : one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym–Green conjecture on syzygies of Prym-canonical...

A quantitative version of the converse Taylor theorem: $C^{k, ω}$ -smoothness

Michal Johanis (2014)

Colloquium Mathematicae

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We prove a uniform version of the converse Taylor theorem in infinite-dimensional spaces with an explicit relation between the moduli of continuity for mappings on a general open domain. We show that if the domain is convex and bounded, then we can extend the estimate up to the boundary.

On the moduli of convexity and smoothness

T. Figiel (1976)

Studia Mathematica

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On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors

Alina Marian, Dragos Oprea (2014)

Annales de l’institut Fourier

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We extend results on generic strange duality for $K 3$ surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized $K 3$ s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized $K 3 s$ .

A remark on a conjecture of Hain and Looijenga

Carel Faber (2011)

Annales de l’institut Fourier

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We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all $g$ and $n$ if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.

Multiple zeta values and periods of moduli spaces ${\bar{𝔐}}_{0, n}$

Francis C. S. Brown (2009)

Annales scientifiques de l'École Normale Supérieure

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We prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces $𝔐_{0, n}$ of Riemann spheres with $n$ marked points are multiple zeta values. We do this by introducing a differential algebra of multiple polylogarithms on $𝔐_{0, n}$ and proving that it is closed under the operation of taking primitives. The main idea is to apply a version of Stokes’ formula iteratively to reduce each period integral to multiple zeta values. We also give a geometric interpretation of the...

Asymptotic behaviour and the moduli space of doubly-periodic instantons

Olivier Biquard, Marcos Jardim (2001)

Journal of the European Mathematical Society

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We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus $T$ with a complex line $ℂ$ , with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to $T \times ℙ^{1}$ . The converse statement is also true, namely a holomorphic bundle on $T \times ℙ^{1}$ which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic...

Singular principal $G$ -bundles on nodal curves

Alexander Schmitt (2005)

Journal of the European Mathematical Society

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In the present paper, we give a first general construction of compactified moduli spaces for semistable $G$ -bundles on an irreducible complex projective curve $X$ with exactly one node, where $G$ is a semisimple linear algebraic group over the complex numbers.

Hyperbolic geometry and moduli of real cubic surfaces

Daniel Allcock, James A. Carlson, Domingo Toledo (2010)

Annales scientifiques de l'École Normale Supérieure

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Let $ℳ_{0}^{ℝ}$ be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space $H^{4}$ and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in $PO (4, 1)$ . We also derive several new and several old results on the topology...

Families of linear differential equations related to the second Painlevé equation

Marius van der Put (2011)

Banach Center Publications

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This paper is a sequel to [vdP-Sa] and [vdP]. The two classes of differential modules (0,-,3/2) and (-,-,3), related to PII, are interpreted as fine moduli spaces. It is shown that these moduli spaces coincide with the Okamoto-Painlevé spaces for the given parameters. The geometry of the moduli spaces leads to a proof of the Painlevé property for PII in standard form and in the Flaschka-Newell form. The Bäcklund transformations, the rational solutions and the Riccati solutions for PII...

The Kodaira dimension of Siegel modular varieties of genus 3 or higher

Eric Schellhammer (2006)

Bollettino dell'Unione Matematica Italiana

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We consider the moduli space $A_{\text{pol}}(n)$ of (non-principally) polarised abelian varieties of genus $g\geq 3$ with coprime polarisation and full level-n structure. Based upon the analysis of the Tits building in [S], we give an explicit lower bound on n that is sufficient for the compactified moduli space to be of general type if one further explicit condition is satisfied.

Bridgeland-stable moduli spaces for $K$ -trivial surfaces

Daniele Arcara, Aaron Bertram (2013)

Journal of the European Mathematical Society

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We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface $S$ and describe “wall-crossing behavior” for objects with the same invariants as $𝒪_{C} (H)$ when $H$ generates Pic $(S)$ and $C \in |H|$ . If, in addition, $S$ is a $K 3$ or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover...

Essential dimension of moduli of curves and other algebraic stacks

Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli (2011)

Journal of the European Mathematical Society

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In this paper we consider questions of the following type. Let $k$ be a base field and $K / k$ be a field extension. Given a geometric object $X$ over a field $K$ (e.g. a smooth curve of genus $g$ ), what is the least transcendence degree of a field of definition of $X$ over the base field $k$ ? In other words, how many independent parameters are needed to define $X$ ? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete...

Bounds on the denominators in the canonical bundle formula

Enrica Floris (2013)

Annales de l’institut Fourier

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In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If $r$ is the Cartier index of the fibre, it was expected that $12 r$ would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in $r$ , we provide a bound $N (r)$ and an example where the smallest integer that clears the denominators of the moduli part is $N (r) / r$ . Moreover we prove that even locally the denominators...