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2-frieze patterns and the cluster structure of the space of polygons

Sophie Morier-Genoud, Valentin Ovsienko, Serge Tabachnikov (2012)

Annales de l’institut Fourier

We study 2-frieze patterns generalizing that of the classical Coxeter-Conway frieze patterns. The geometric realization of this space is the space of $n$ -gons (in the projective plane and in 3-dimensional vector space) which is a close relative of the moduli space of genus $0$ curves with $n$ marked points. We show that the space of 2-frieze patterns is a cluster manifold and study its algebraic and arithmetic properties.

3-dimensional sundials

Enrico Carlini, Maria Catalisano, Anthony Geramita (2011)

Open Mathematics

R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).

3-Folds in P5 of Degree 12.

Gerhard Edelmann (1994)

Manuscripta mathematica

A 2-dimensional Algebraic Variety With 27 Rectilinear Generators and 108 Trisecants and its Connection With the Maximal Exceptional Simple lie Group

Boris Rosenfeld (2005)

Publications de l'Institut Mathématique

A bound for the degree of smooth surfaces in $P^{4}$ not of general type

Robert Braun, Gunnar Fløystad (1994)

Compositio Mathematica

A bound for the Milnor number of plane curve singularities

Arkadiusz Płoski (2014)

Open Mathematics

Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].

Currently displaying 1 – 20 of 561

Page 1 Next

Displaying 1 – 20 of 561

2-frieze patterns and the cluster structure of the space of polygons

3-dimensional sundials

3-Folds in P5 of Degree 12.

A 2-dimensional Algebraic Variety With 27 Rectilinear Generators and 108 Trisecants and its Connection With the Maximal Exceptional Simple lie Group

A bound for the degree of smooth surfaces in $P^{4}$ not of general type

A bound for the Milnor number of plane curve singularities

A bound of the degree of some rational surfaces in $ℙ^{4}$ .

A bound on the geometric genus of projective varieties

A Castelnuovo bound for smooth surfaces.

A Characterization of Balanced Rational Normal Surface Scrolls in Terms of Their Osculating Spaces II.

A characterziation of IPn by vector bundles.

A conjecture on Poincaré-Betti series of modules of differential operators on a generic hyperplane arrangement.

A criterion for the ideal of a projectively embedded toric surface to be generated by quadrics.

A Decomposability Criterion for Algebraic 2-Bundles on Projective Spaces.

A descendent relation in genus 2

A Geometrical approach to Gordan--Noether's and Franchetta's contributions to a question posed by Hesse.

A linear bound on the t-normality of codimension two subvarieties of ...n.

A mathematical proof of a formula of Aspinwall and Morrison

A modular compactification of the general linear group.

A new construction of a surface of degree $5$ having $31$ nodes

Currently displaying 1 – 20 of 561