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