Results 41 to 50 of about 1,986 (102)
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
New symplectic V-manifolds of dimension four via the relative compactified Prymian [PDF]
, 2007 Three new examples of 4-dimensional irreducible symplectic V-manifolds are constructed. Two of them are relative compactified Prymians of a family of genus-3 curves with involution, and the third one is obtained from a Prymian by Mukai's flop.
Markushevich, D., Tikhomirov, A. S.
core +2 more sources
, 2007 We prove that Prym varieties are characterized geometrically by the existence of a symmetric pair of quadrisecant planes of the associated Kummer variety. We also show that Prym varieties are characterized by certain (new) theta-functional equations. For
Grushevsky, Samuel, Krichever, Igor
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Cyclic coverings of genus $2$ curves of Sophie Germain type
Forum of Mathematics, SigmaWe 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
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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
Prym varieties and integrable systems [PDF]
Communications in Analysis and Geometry, 1997 In this article a new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of \(GL_n\) defined on certain infinite-dimensional Grassmannians is studied. H. Morikawa's question is: What are the finite-dimensional orbits of
Li, Yingchen, Mulase, Mothico
openaire +2 more sources
Spin(8,
MathematicsLet 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
Secants of Abelian Varieties, Theta functions, and Soliton Equations
, 1996 This paper is a survey on relations between secant identities and soliton equations and applications of soliton equations to problems of algebraic geometry, i.e., the Riemann-Schottky problem and its analogues.
Taimanov, I. A.
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The geometry and arithmetic of bielliptic Picard curves
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley +1 more source
Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
wiley +1 more source