Codimension two transcendental submanifolds of projective space

Wojciech Kucharz; Santiago R. Simanca

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Homology classes of real algebraic sets

Wojciech Kucharz (2008)

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There is a large research program focused on comparison between algebraic and topological categories, whose origins go back to 1952 and the celebrated work of J. Nash on real algebraic manifolds. The present paper is a contribution to this program. It investigates the homology and cohomology classes represented by real algebraic sets. In particular, such classes are studied on algebraic models of smooth manifolds.

On approximation of smooth submanifolds by nonsingular real algebraic subvarieties

Jacek Bochnak, Wojciech Kucharz (2003)

Annales scientifiques de l'École Normale Supérieure

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Numerical character of the effectivity of adjoint line bundles

Frédéric Campana, Vincent Koziarz, Mihai Păun (2012)

Annales de l’institut Fourier

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In this note we show that, for any log-canonical pair $(X, Δ)$ , $K_{X} + Δ$ is $ℚ$ -effective if its Chern class contains an effective $ℚ$ -divisor. Then, we derive some direct corollaries.

Vector bundles over real algebraic surfaces and threefolds

Wojciech Kucharz (1986)

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Low pole order frames on vertical jets of the universal hypersurface

Joël Merker (2009)

Annales de l’institut Fourier

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For low order jets, it is known how to construct meromorphic frames on the space of the so-called vertical $k$ -jets $J_{vert}^{k} (𝒳)$ of the universal hypersurface $𝒳 \subset ℙ^{n + 1} \times ℙ^{\frac{(n + 1 + d)!}{((n + 1)! d!)} - 1}$ parametrizing all projective hypersurfaces $X \subset ℙ^{n + 1} (ℂ)$ of degree $d$ . In 2004, for $k = n$ , Siu announced that there exist two constants $c_{n} \geq 1$ and $c_{n}^{'} \geq 1$ such that the twisted tangent bundle $T_{J_{vert}^{n} (𝒳)} \otimes 𝒪_{ℙ^{n + 1}} (c_{n}) \otimes 𝒪_{ℙ^{\frac{(n + 1 + d)!}{((n + 1)! d!)} - 1}} (c_{n}^{'})$ is generated at every point by its global sections. In...