Monomial embeddings of the Klein curve

Singularities of the Hypergeometric System Associated with a Monomial Curve

We compute, using D-module restrictions, the slopes of the irregular hypergeometric system associated with a monomial curve. We also study rational solutions and reducibility of such systems.

The -hypergeometric System Associated with a Monomial Curve

Introduction. In this paper we make a detailed analysis of the -hypergeometric system (or GKZ system) associated with a monomial curve and integral, hence resonant, exponents. We describe all rational solutions and show in Theorem 1.10 that they are, in fact, Laurent polynomials. We also show that for any exponent there are at most two linearly independent Laurent solutions and that the upper b...

Spanning subsets of toroidal and Klein bottle embeddings

Let Φ be an embedding of graph G in a surface S. If there exists a subset K of S bounded by a subgraph of G which contains all the vertices of G, then K is called a spanning subset of Φ. Examples of spanning subsets include spanning discs, spanning annuli with some number of holes (called planarizing sets in some papers). A spanning subset may provide a simpler structure but still contain enoug...

Slopes of a Hypergeometric System Associated to a Monomial Curve

where () means “transpose”. We denote by θ the vector (θ1, . . . , θn) T with θi = xi∂i. For a given β = (β1, . . . , βd) T ∈ C we consider the column vector (in An) Aθ−β and we denote by 〈Aθ − β〉 the left ideal of An generated by the entries of Aθ − β. Following Gel’fand, Kapranov and Zelevinsky [6], we denote by HA(β) the left ideal of An generated by IA∪〈Aθ−β〉. It is called the GKZ-hypergeom...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION