Abelian varieties and Riemann surfaces with generalized quaternion group action
نویسندگان
چکیده
We consider abelian varieties with a group of automorphisms isomorphic to generalized quaternion group. provide isogeny decompositions, compute dimensions the corresponding factors and give conditions under which this decomposition is nontrivial. then specialize our results Jacobians relate them so-called genus-zero actions on Riemann surfaces. A complete classification uniparametric families surfaces action given, extending known for quasiplatonic case. Finally, we construct explicit derive period matrix Jacobian surface full automorphism second largest order among hyperelliptic genus four.
منابع مشابه
un 2 00 1 Abelian varieties with group action
Introduction. Let G be a finite group acting on a smooth projective curve X. This induces an action of G on the Jacobian JX of X and thus a decomposition of G of JX up to isogeny. The most prominent example of such a situation is the case of the group G ≃ Z/2Z of two elements. Let π : X → Y = X/G denote the canonical quotient map. The first to notice that JX is isogenous to the product JY × P (...
متن کاملNon-abelian vortices on compact Riemann surfaces
We consider the vortex equations for a U(n) gauge field A coupled to a Higgs field φ with values on the n × n matrices. It is known that when these equations are defined on a compact Riemann surface Σ, their moduli space of solutions is closely related to a moduli space of τ -stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the matrix φ, we show t...
متن کاملAbelian Gauge Theory on Riemann Surfaces
An Abelian gauge eld theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the rst Chern class c 1 (L) and by a certain intersection number obtained fro...
متن کاملGeneralized Quadrangles with an Abelian Singer Group
In this note we characterize thick finite generalized quadrangles constructed from a generalized hyperoval as those admitting an abelian Singer group, i.e., an abelian group acting regularly on the points.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2023
ISSN: ['1873-1376', '0022-4049']
DOI: https://doi.org/10.1016/j.jpaa.2023.107398