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Nagata submaximal curves on ℙ¹ × ℙ¹

Wioletta Syzdek (2003)

Annales Polonici Mathematici

The aim of this paper is to show that on ℙ¹ × ℙ¹ with a polarization of type (2,1) there are no R-R expected submaximal curves through any 10 ≤ r ≤ 15 points.

Nakamaye’s theorem on log canonical pairs

Salvatore Cacciola, Angelo Felice Lopez (2014)

Annales de l’institut Fourier

We generalize Nakamaye’s description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension ≤ 1 . We also generalize Ein-Lazarsfeld-Mustaţă-Nakamaye-Popa’s description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.

Nash cohomology of smooth manifolds

W. Kucharz (2005)

Annales Polonici Mathematici

A Nash cohomology class on a compact Nash manifold is a mod 2 cohomology class whose Poincaré dual homology class can be represented by a Nash subset. We find a canonical way to define Nash cohomology classes on an arbitrary compact smooth manifold M. Then the Nash cohomology ring of M is compared to the ring of algebraic cohomology classes on algebraic models of M. This is related to three conjectures concerning algebraic cohomology classes.

Nonabelian Hodge theory in characteristic p

A. Ogus, V. Vologodsky (2007)

Publications Mathématiques de l'IHÉS

Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.

Non-obstructed subcanonical space curves.

Rosa M. Miró-Roig (1992)

Publicacions Matemàtiques

Recall that a closed subscheme X ⊂ P is non-obstructed if the corresponding point x of the Hilbert scheme Hilbp(t)n is non-singular. A geometric characterization of non-obstructedness is not known even for smooth space curves. The goal of this work is to prove that subcanonical k-Buchsbaum, k ≤ 2, space curves are non-obstructed. As a main tool we use Serre's correspondence between subcanonical curves and vector bundles.

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