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On the number of compatibly Frobenius split subvarieties, prime F -ideals, and log canonical centers

Karl Schwede, Kevin Tucker (2010)

Annales de l’institut Fourier

Let X be a projective Frobenius split variety with a fixed Frobenius splitting θ . In this paper we give a sharp uniform bound on the number of subvarieties of X which are compatibly Frobenius split with θ . Similarly, we give a bound on the number of prime F -ideals of an F -finite F -pure local ring. Finally, we also give a bound on the number of log canonical centers of a log canonical pair. This final variant extends a special case of a result of Helmke.

On triple curves through a rational triple point of a surface

M. R. Gonzalez-Dorrego (2006)

Annales Polonici Mathematici

Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.

Plane curve singularities and carousels

Lê Dung Tráng (2003)

Annales de l’institut Fourier

In this paper we give a direct and explicit description of the local topological embedding of a plane curve singularity using the Puiseux expansions of its branches in a given set of coordinates.

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