Results 31 to 40 of about 105 (95)

Isogenies of Prym varieties

Le Matematiche, 2017
We prove an extension of the Babbage-Enriques-Petri theorem for semi-canonical curves. We apply this to show that the Prym variety of a generic element of a codimension $k$ subvariety of $\kr_g$ is not isogenous to another distinct Prym variety, under some mild assumption on $k$.
Roberto Laface, César Martínez
openaire   +1 more source

The Hodge conjecture for general Prym varieties [PDF]

Journal of Algebraic Geometry, 2001
We calculate the Mumford-Tate group of the general Prym variety. As a consequence, the algebra of Hodge cycles is generated by the Néron-Severi.
Biswas, Indranil, Paranjape, Kapil H.
openaire   +2 more sources

Étude géométrique et topologique du flot géodésique sur le groupe des rotations [PDF]

Surveys in Mathematics and its Applications, 2016
The aim of this survey paper is to investigate the algebraic complete integrability of Euler-Arnold's body description of the four dimensional rigid body, or equivalently of geodesics in SO(4) using left-invariant metrics that arise from inertia tensors,
Ahmed Lesfari
doaj  

Prym varieties of spectral covers [PDF]

Geometry & Topology, 2012
Given a possibly reducible and non-reduced spectral cover X over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(X/C). As an immediate application we show that the finite group of n-torsion points of the Jacobian of C acts trivially on the cohomology of the twisted SL_n-Higgs moduli space up ...
Hausel, Tamás, Pauly, Christian
openaire   +3 more sources

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

Spectral theory and nonlinear problems Théorie spectrale et problèmes non-linéaires [PDF]

Surveys in Mathematics and its Applications, 2010
We present a Lie algebra theoretical schema leading to integrable systems, based on the Kostant-Kirillov coadjoint action. Many problems on Kostant-Kirillov coadjoint orbits in subalgebras of infinite dimensional Lie algebras (Kac-Moody Lie algebras)
Ahmed Lesfari
doaj  

Spin(8,$\mathbb{C}$)-Higgs Bundles and the Hitchin Integrable System

Mathematics
Let M(Spin(8,C)) be the moduli space of Spin(8,C)-Higgs bundles over a compact Riemann surface X of genus g≥2. This admits a system called the Hitchin integrable system, induced by the Hitchin map, the fibers of which are Prym varieties.
Álvaro Antón-Sancho
doaj   +1 more source

Motivic mirror symmetry and χ$\chi$‐independence for Higgs bundles in arbitrary characteristic

Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.
Abstract We prove that the (twisted orbifold) motives of the moduli spaces of SLn$\mathrm{SL}_n$ and PGLn$\mathrm{PGL}_n$‐Higgs bundles of coprime rank and degree on a smooth projective curve over an algebraically closed field in which the rank is invertible are isomorphic in Voevodsky's triangulated category of motives.
Victoria Hoskins, Simon Pepin Lehalleur
wiley   +1 more source

Fourier transform and Prym varieties

Journal für die reine und angewandte Mathematik (Crelles Journal), 2003
Let $P$ be the Prym variety attached to an unramified double covering $\tilde{C} \rightarrow C$. Let $X=X(\tilde{\boldsymbol{C}}, C)$ be the variety of special divisors which birationally parametrizes the theta divisor in $P$. We prove that $X$ is the projectivization of the Fourier-Mukai transform of a coherent sheaf $p_*(M)$, where $M$ is an ...
openaire   +2 more sources

Wild conductor exponents of curves

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We give an explicit formula for wild conductor exponents of plane curves over Qp$\mathbb {Q}_p$ in terms of standard invariants of explicit extensions of Qp$\mathbb {Q}_p$, generalising a formula for hyperelliptic curves. To do so, we prove a general result relating the wild conductor exponent of a simply branched cover of the projective line ...
Harry Spencer
wiley   +1 more source