Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

We already have the concept of isotropicity of a minimal surface in a Riemannian 4-manifold and a space-like or time-like surface in a neutral 4-manifold with zero mean curvature vector. In this paper, based on the understanding of it, we define and study isotropicity of a space-like or time-like surface in a Lorentzian 4-manifold N with zero mean curvature vector. If the surface is space-like, then the isotropicity means either the surface has light-like or zero second fundamental form or it is an analogue of complex curves in Kähler surfaces. In addition, if N is a space form, then the isotropicity means that the surface has both the properties. If the surface is time-like and if N is a space form, then the isotropicity means that the surface is totally geodesic.

It is proved that decomposable graphs are set recognizable and that the index graph of the canonical decomposition as well as the graphs induced on the maximal autonomous sets of vertices are set reconstructible. From these results, we obtain set reconstructibility for many decomposable graphs as well as a concise description of the decomposable graphs for which set reconstruction remains an open problem.

We study sign changes and non-vanishing of a certain double sequence of Fourier coefficients of cusp forms of half-integral weight.

Combining theorems of Voisin and Marian, Shen, Yin and Zhao, we compute the dimensions of the orbits under rational equivalence in the Mukai system of rank two and genus two. We produce several examples of algebraically coisotropic and constant cycle subvarieties.

We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over (mathbb {F}_q), conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.

In this paper, we consider a kind of area-preserving flow for closed convex planar curves which will decrease the length of the evolving curve and make the evolving curve more and more circular during the evolution process. And the final shape of the evolving curve will be a circle as time (trightarrow +infty ).

Let X be a smooth quintic hypersurface in (mathbb {P}^3), let C be a smooth hyperplane section of X, and let (H=mathcal {O}_X(C)). In this paper, we give a necessary and sufficient condition for the line bundle given by a non-zero effective divisor on X to be initialized and aCM with respect to H.

We study p-adic L-functions (L_p(s,chi )) for Dirichlet characters (chi ). We show that (L_p(s,chi )) has a Dirichlet series expansion for each regularization parameter c that is prime to p and the conductor of (chi ). The expansion is proved by transforming a known formula for p-adic L-functions and by controlling the limiting behavior. A finite number of Euler factors can be factored off in a natural manner from the p-adic Dirichlet series. We also provide an alternative proof of the expansion using p-adic measures and give an explicit formula for the values of the regularized Bernoulli distribution. The result is particularly simple for (c=2), where we obtain a Dirichlet series expansion that is similar to the complex case.

The moduli spaces of flat ({text{SL}}_2)- and ({text{PGL}}_2)-connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.