116063399
On elementary transformations of ruled surfaces.
In classical literature a ruled surface means a surface F in some projective space with a one dimensional family of lines lying on it. An elementary transformation then is a linear projection with a smooth point of the surface s center. Considering only nonsingular non-embedded models, every ruled surface is of the form P (E) with a vector b ndle E of rank 2 on a nonsingular projective curve X say of genus g over a field k which we assume to be algebraically closed. Abstractly an elementary transformation is the composition of the blowing up of a point P of P(E) and the blowing down of the proper transform of the fibre π"" (π (P)), where π: Ρ(Ε)-+Χ means the natural map. The resulting surface again is a ruled surface which we denote by elmp (P (E)). Inductively we define elmFl. ..Pn (P (£")):= elmPn(elmFl...Pn _{ (P (E))). It is easy to see that every ruled surface over X can be obtained by a finite number of elementary transformations starting with the trivial ruled surface XxP. Hence it makes sense to consider the following invariant (cf. [1], [2], [3]): n(P(E)):= the minimum n such that there are points P!,..., P„ with P(£)^elmPi...Pn( r x P). In [1], [2], and [3] Nagata and Maruyama proved the following
122360469
Commutative algebraic groups and intersections of quadrics
Let E be a commutative connected algebraic group over a field k. The purpose of this paper is to construct embeddings of E into some pN such that the homogeneous ideal of the closure E of E in ~,u is generated by quadratic forms. In particular such an E is idealtheoretically an intersection of quadrics. To outline a special case let k be the field of complex numbers and consider the canonical exact sequence O-~G ~ E-~ A ~O
117841059
Arithmetic of Complex Manifolds: Proceedings of a Conference Held in Erlangen, Frg, May 27-31 1988
Surfaces on quintic threefolds associated to the Horrocks-Mumford bundle.- Curves of genus three on a general abelian threefold and the non-finite generation of the Griffiths group.- Sur les fonctions theta du second ordre.- Une demonstration elementaire du theoreme de Torelli pour les intersections de trois quadriques generiques de dimension impaire.- Nodal quintics in P4.- Volumes of fundamental domains of Picard modular groups.- The siegel modular variety of degree two and level four: A report.- Some effective estimates for elliptic curves.- A pencil of K3- surfaces related to Apery's recurrence for ?(3) and Fermi surfaces for potential zero.- The work of kolyvagin on the arithmetic of elliptic curves.- Cyclic covers of Pv branched along v + 2 hyperplanes and the generalized Hodge Conjecture for certain abelian varieties.- On the cohomology of siegel modular threefolds.
201061914
Über die Modulschemata der Kurven vom Geschlecht 2 mit 1, 2 oder 3 Weierstraßpunkten.
121664953
Some remarks on compactifications of commutative algebraic groups
121963238
Die globale Lösbarkeit einer nichtlinearen Reaktionsgleichung
122361054
On nonlinear Schrödinger equations in the theory of quantum mechanical dissipative systems
On resout le probleme de Cauchy iΨ u t=HΨ avec H=―h 2 δ 2 /2mδ 2 x+ω 2 x 2 /2+γW(Ψ) (γ=cte) par une methode de developpement de Galerkin en utilisant les fonctions propres de l'oscillateur harmonique. On peut montrer que le probleme aux valeurs initiales non lineaire a une dimension d'espace iΨ t =HΨ, Ψ(x,0)=Ψ 0 (x) a des solutions faibles globales determinees de facon unique