Results 61 to 70 of about 3,771 (225)

Heights on stacks and a generalized Batyrev–Manin–Malle conjecture

Forum of Mathematics, Sigma, 2023
We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties.
Jordan S. Ellenberg, Matthew Satriano, David Zureick-Brown   +2 more
doaj   +1 more source

Totally elliptic surface group representations

Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.
Abstract A surface group representation into a Lie group is totally elliptic if every simple closed curve on the surface is mapped to an elliptic element. In this note, we characterize all totally elliptic surface group representations into PSL2R$\operatorname{PSL}_2 \mathbb {R}$ and PSL2C$\operatorname{PSL}_2\mathbb {C}$ by showing that they are ...
Arnaud Maret
wiley   +1 more source

Generalized algebraic completely integrable systems [PDF]

Surveys in Mathematics and its Applications, 2020
We tackle in this paper the study of generalized algebraic completely integrable systems. Some interesting cases of integrable systems appear as coverings of algebraic completely integrable systems.
Ahmed Lesfari
doaj  

The size function of abelian varieties [PDF]

Transactions of the American Mathematical Society, 1972
The size function is defined for points in projective space over any field K , finitely generated field over Q , generalizing the height function for number fields.
openaire   +2 more sources

A birational description of the minimal exponent

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We give a description of the minimal exponent of a hypersurface using higher direct images of suitably twisted sheaves of log forms on a log resolution.
Qianyu Chen, Mircea Mustaţă
wiley   +1 more source

Cyclic coverings of genus $2$ curves of Sophie Germain type

Forum of Mathematics, Sigma
We consider cyclic unramified coverings of degree d of irreducible complex smooth genus $2$ curves and their corresponding Prym varieties. They provide natural examples of polarized abelian varieties with automorphisms of order d.
J.C. Naranjo, A. Ortega, I. Spelta
doaj   +1 more source

The Picard Group of the Universal Abelian Variety and the Franchetta Conjecture for Abelian Varieties [PDF]

Michigan Mathematical Journal, 2019
We compute the Picard group of the universal abelian variety over the moduli stack $\mathscr A_{g,n}$ of principally polarized abelian varieties over $\mathbb{C}$ with a symplectic principal level $n$-structure. We then prove that over $\mathbb{C}$ the statement of the Franchetta conjecture holds in a suitable form for $\mathscr A_{g,n}$.
Fringuelli R., Pirisi R.
openaire   +5 more sources

Heights on ‘hybrid orbits’ in Shimura varieties

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract We prove the ‘hybrid conjecture’ which is a common generalisation of the André–Oort conjecture and the André–Pink–Zannier conjecture, in the case of Shimura varieties of abelian type.
Rodolphe Richard, Andrei Yafaev
wiley   +1 more source

Finding maximal torsion cosets on varieties [PDF]

, 2007
We describe a new algorithm for finding all maximal torsion cosets on varieties over $\G_m^n$. We illustrate the algorithm with some examples.The starting point for this study is the search for points on a given variety whose coordinates are roots of ...
Aliev, Iskander, Smyth, Christopher
core