manuscripta mathematica

Let R be a commutative noetherian ring with unit. To a sequencex:=x1,...,xn of elements of R and an m-by-n matrix α:=(αij) with entries in R we assign a complex D*(x;α), in case that m=n or m=n−1. These complexes will provide us in certain cases with explicit minimal free resolutions of ideals, which are generated by the elements ai:=∑αijxj and the maximal minors of α.

We present an asymptotic analysis for the solution of period 4 of $$\dot x(t) = - \alpha f(x(t - 1))$$ , where f is an odd function and α a positive parameter.

The lowest dimensional Jacobi groupG J sets a link between the theory of Siegel modular forms of degree two and the elliptic modular forms of integral and half integral weight. This note is meant to help finding a way to associateL-functions to automorphic representations of the groupG J by using the approach via Whittaker models of these representations. Thus, here the question of existence and unicity of these models is discussed. This question may be reduced to a closer study of the Schrödinger and Weil representation of the Heisenberg resp. the metaplectic group and thus to the application of some results by Waldspurger.

We consider nonlinear elliptic equations driven by the p-Laplacian differential operator. Using degree theoretic arguments based on the degree map for operators of type (S)+ , we prove theorems on the existence of multiple nontrivial solutions of constant sign.

We describe the relationship between closed affine laminations in a punctured surface and some associated hyperbolic structures on certain covers of the punctured surface, which we call covering hyperbolic structures. Further, in analogy with the theory of William Thurston relating the Teichmüller space of a surface to the projective lamination space, we describe a space with points representing affine laminations in a given surface and with other points representing the associated covering hyperbolic structures.

We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface S, defined over a number field K and satisfying $$S^{[2]}(K) \neq \emptyset$$ , then X has a model over K such that the L-series of the primitive cohomology of X/K can be expressed in terms of the L-series of S/K. This allows us to compute the L-series for a discrete dense subset of cubic fourfolds in the moduli spaces of certain special cubic fourfolds. We also discuss a concrete example.

A Coincidence index in any generalized (multiplicative) cohomology theory is defined for certain pairs of maps between euclidean neighborhood retracts over a metric space B. By taking an adequate geometric equivalence relation between two such coincidence situations, groups FIXk (B) and FIXk (B,A), for A closed in B, k an integer, can be defined. The purpose of this paper is to show that these groups constitute a generalized multiplicative cohomology theory. Moreover, we show that the index determines an isomorphism between this theory and stable cohomotopy.

We present some rational elliptic surfaces over a certain field such that certain open subschemes do not satisfy the surjectivity of the boundary map on K 2 arising from the localization sequence. We consider two cases that the base field is transcendental over its prime subfield and that the base field is characteristic zero.

Let I denote an ideal of a local Gorenstein ring $${(R, \mathfrak m)}$$ . Then we show that the local cohomology module $${H^c_I(R)}$$ , c = height I, is indecomposable if and only if V(I d ) is connected in codimension one. Here I d denotes the intersection of the highest dimensional primary components of I. This is a partial extension of a result shown by Hochster and Huneke in the case I the maximal ideal. Moreover there is an analysis of connectedness properties in relation to various aspects of local cohomology. Among others we show that the endomorphism ring of $${H^c_I(R)}$$ is a local Noetherian ring if dim R/I  =  1.