Search results for " Geometry."

Hurwitz spaces of Galois coverings of P1, whose Galois groups are Weyl groups

2006

Abstract We prove the irreducibility of the Hurwitz spaces which parametrize equivalence classes of Galois coverings of P 1 , whose Galois group is an arbitrary Weyl group, and the local monodromies are reflections. This generalizes a classical theorem due to Luroth, Clebsch and Hurwitz.

On Shimura subvarieties generated by families of abelian covers ofP1

2018

We investigate the occurrence of Shimura (special) subvarieties in the locus of Jacobians of abelian Galois covers of P1 in Ag and give classifications of families of such covers that give rise to Shimura subvarieties in the Torelli locus Tg inside Ag. Our methods are based on Moonen–Oort works as well as characteristic p techniques of Dwork and Ogus and Monodromy computations.

An exact and efficient approach for computing a cell in an arrangement of quadrics

2006

AbstractWe present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected plana…

Symplectic automorphisms of prime order on K3 surfaces

2006

The aim of this paper is to study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients. We determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. We also compute many explicit examples, with particular attention to elliptic fibrations.

Quantum extensions of semigroups generated by Bessel processes

1996

We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).

Functional Calculus and Fredholm Criteria for Boundary Value Problems on Noncompact Manifolds

1992

A Boutet de Monvel type calculus is developed for boundary value problems on (possibly) noncompact manifolds. It is based on a class of weighted symbols and Sobolev spaces. If the underlying manifold is compact, one recovers the standard calculus. The following is proven:

A note on projective coordinate systems of modular lattices

1993

This note clarifies the combinatorial nature of projective coordinate systems of modular upper continuous lattices. It generalizes the classical relationship between 3-dimensional Desarguesian configurations and coordinate systems of projective 3-spaces.

Projective Geometry on Modular Lattices

1995

Publisher Summary This chapter focuses on projective geometry on modular lattices. Incidence and Order are basic concepts for a foundation of modern synthetic geometry. These concepts describe the relative location or containment of geometric objects and have led to different lines of geometry, an incidence-geometric and a lattice-theoretic one. Modularity is one of the fundamental properties of classical projective geometry. It makes projections into join-preserving mappings and yields perspectivities to be (interval) isomorphisms. It is therefore natural that order-theoretic generalizations of projective geometry are based on modular lattices and even more, the theory of modular lattices …

General measure theory

1995

Linear invariants of Riemannian almost product manifolds

1982

Using the decomposition of a certain vector space under the action of the structure group of Riemannian almost product manifolds, A. M. Naveira (9) has found thirty-six distinguished classes of these manifolds. In this article, we prove that this decomposition is irreducible by computing a basis of the space of invariant quadratic forms on such a space.