Displaying similar documents to “On the motives of moduli of chains and Higgs bundles”

Asymptotic behaviour and the moduli space of doubly-periodic instantons

Olivier Biquard, Marcos Jardim (2001)

Journal of the European Mathematical Society

Similarity:

We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line , 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 × 1 . The converse statement is also true, namely a holomorphic bundle on T × 1 which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic...

Limiting configurations for solutions of Hitchin’s equation

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

Séminaire de théorie spectrale et géométrie

Similarity:

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...

The Kodaira dimension of the moduli space of Prym varieties

Gavril Farkas, Katharina Ludwig (2010)

Journal of the European Mathematical Society

Similarity:

We study the enumerative geometry of the moduli space g of Prym varieties of dimension g - 1 . Our main result is that the compactication of 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 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...

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

Similarity:

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

The tautological ring of M 1 , n c t

Mehdi Tavakol (2011)

Annales de l’institut Fourier

Similarity:

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.

Singular principal G -bundles on nodal curves

Alexander Schmitt (2005)

Journal of the European Mathematical Society

Similarity:

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.

Moduli of smoothness of functions and their derivatives

Z. Ditzian, S. Tikhonov (2007)

Studia Mathematica

Similarity:

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.

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

Eric Schellhammer (2006)

Bollettino dell'Unione Matematica Italiana

Similarity:

We consider the moduli space A pol ( n ) of (non-principally) polarised abelian varieties of genus g 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.

On non-basic Rapoport-Zink spaces

Elena Mantovan (2008)

Annales scientifiques de l'École Normale Supérieure

Similarity:

In this paper we study certain moduli spaces of Barsotti-Tate groups constructed by Rapoport and Zink as local analogues of Shimura varieties. More precisely, given an isogeny class of Barsotti-Tate groups with unramified additional structures, we investigate how the associated (non-basic) moduli spaces compare to the (basic) moduli spaces associated with its isoclinic constituents. This aspect of the geometry of the Rapoport-Zink spaces is closely related to Kottwitz’s prediction that...

Bounds on the denominators in the canonical bundle formula

Enrica Floris (2013)

Annales de l’institut Fourier

Similarity:

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...

A remark on a conjecture of Hain and Looijenga

Carel Faber (2011)

Annales de l’institut Fourier

Similarity:

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.

Essential dimension of moduli of curves and other algebraic stacks

Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli (2011)

Journal of the European Mathematical Society

Similarity:

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...

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

Alina Marian, Dragos Oprea (2014)

Annales de l’institut Fourier

Similarity:

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 .

Multiple zeta values and periods of moduli spaces 𝔐 ¯ 0 , n

Francis C. S. Brown (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

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...

Notes on prequantization of moduli of G -bundles with connection on Riemann surfaces

Andres Rodriguez (2004)

Annales mathématiques Blaise Pascal

Similarity:

Let 𝒳 S be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and a G -bundle over 𝒳 with connection along the fibres 𝒳 S . We construct a line bundle with connection ( , ) on S (also in cases when the connection on has regular singularities). We discuss the resulting ( , ) mainly in the case G = * . For instance when S is the moduli space of line bundles with connection over a Riemann surface X , 𝒳 = X × S , and is the Poincaré bundle over 𝒳 , we show that ( , ) provides a prequantization...

A quantitative version of the converse Taylor theorem: C k , ω -smoothness

Michal Johanis (2014)

Colloquium Mathematicae

Similarity:

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.

Bridgeland-stable moduli spaces for K -trivial surfaces

Daniele Arcara, Aaron Bertram (2013)

Journal of the European Mathematical Society

Similarity:

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 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...