Die Zerlegungscharaktere abelscher total reeller Erweiterungen reeller Funktionenkörper einer Variablen.
Dimensions of Prym varieties.
Distinguishing Prymians from Jacobians.
Ein Beweis des Additionstheorems für die hyperelliptischen Integrale
Eine Verallgemeinerung des Satzes von Castelnuovo-Severi.
Endomorphisms of jacobian varieties of Fermat curves
Explicit descent for Jacobians of cyclic coevers of the projective line.
Explicit Selmer groups for cyclic covers of ℙ¹
For any abelian variety J over a global field k and an isogeny ϕ: J → J, the Selmer group is a subgroup of the Galois cohomology group , defined in terms of local data. When J is the Jacobian of a cyclic cover of ℙ¹ of prime degree p, the Selmer group has a quotient by a subgroup of order at most p that is isomorphic to the ‘fake Selmer group’, whose definition is more amenable to explicit computations. In this paper we define in the same setting the ‘explicit Selmer group’, which is isomorphic...
Faltings modular height and self-intersection of dualizing sheaf.
Finite subschemes of abelian varieties and the Schottky problem
The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties of dimension , by the existence of points in special position with respect to , but general with respect to , and furthermore states that such collections of points must be contained in an Abel-Jacobi curve. Building on the ideas in the original paper, we give here a self contained, scheme theoretic proof of the theorem, extending it to finite, possibly...
Fonctions theta du second ordre sur la jacobienne d'une courbe lisse.
For which Jacobi varities is Sing ... reducible?
Form Factors, KdV and Deformed Hyperelliptic Curves
Formal group laws for certain formal groups arising from modular curves
Formal groups in genus two.
Generalised elliptic functions
We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstraß ℘-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed...
Generalization of Abel's theorem and some finiteness property of zero-cycles on surfaces
Generalized Weierstrass ...-functions and KP flows in affine spaces.
Geometry of the theta divisor of a compactified jacobian
Group actions on Jacobian varieties.