13,254 research outputs found
Characterizing the Delaunay decompositions of compact hyperbolic surfaces
Given a Delaunay decomposition of a compact hyperbolic surface, one may
record the topological data of the decomposition, together with the
intersection angles between the `empty disks' circumscribing the regions of the
decomposition. The main result of this paper is a characterization of when a
given topological decomposition and angle assignment can be realized as the
data of an actual Delaunay decomposition of a hyperbolic surface.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol6/paper12.abs.htm
Syzygies and singularities of tensor product surfaces of bidegree (2,1)
Let U be a basepoint free four-dimensional subspace of the space of sections
of O(2,1) on P^1 x P^1. The sections corresponding to U determine a regular map
p_U: P^1 x P^1 --> P^3. We study the associated bigraded ideal I_U in
k[s,t;u,v] from the standpoint of commutative algebra, proving that there are
exactly six numerical types of possible bigraded minimal free resolution. These
resolutions play a key role in determining the implicit equation of the image
p_U(P^1 x P^1), via work of Buse-Jouanolou, Buse-Chardin, Botbol and
Botbol-Dickenstein-Dohm on the approximation complex. In four of the six cases
I_U has a linear first syzygy; remarkably from this we obtain all differentials
in the minimal free resolution. In particular this allows us to describe the
implicit equation and singular locus of the image.Comment: 35 pages 1 figur
The cohomology rings of the unordered configuration spaces of the torus
We study the cohomology ring of the configuration space of unordered points
in the two dimensional torus. In particular, we compute the mixed Hodge
structure on the cohomology, the action of the mapping class group, the
structure of the cohomology ring and we prove the formality over the rationals.Comment: This was part of arXiv:1805.04906v2 (section 4), 13 pages, 1 figur
Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory
International audienceIn the Teichmüller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to reparametrization). The lines we construct are special stretch lines in the sense of Thurston. They are directed by complete geodesic laminations that are not chain-recurrent, and they have a nice description in terms of Fenchel-Nielsen coordinates. At the basis of the construction are certain maps with controlled Lipschitz constants between right-angled hyperbolic hexagons having three non-consecutive edges of the same size. Using these maps, we obtain Lipschitz-minimizing maps between hyperbolic particular pairs of pants and, more generally, between some hyperbolic sufaces of finite type with arbitrary genus and arbitrary number of boundary components. The Lipschitz-minimizing maps that we contruct are distinct from Thurston's stretch maps
Sums of residues on algebraic surfaces and application to coding theory
In this paper, we study residues of differential 2-forms on a smooth
algebraic surface over an arbitrary field and give several statements about
sums of residues. Afterwards, using these results we construct
algebraic-geometric codes which are an extension to surfaces of the well-known
differential codes on curves. We also study some properties of these codes and
extend to them some known properties for codes on curves.Comment: 31 page
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