Displaying similar documents to “On homology classes represented by real algebraic varieties”

Homology classes of real algebraic sets

Wojciech Kucharz (2008)

Annales de l’institut Fourier

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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.

The optimality of the Bounded Height Conjecture

Evelina Viada (2009)

Journal de Théorie des Nombres de Bordeaux

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In this article we show that the Bounded Height Conjecture is optimal in the sense that, if V is an irreducible subvariety with empty deprived set in a power of an elliptic curve, then every open subset of V does not have bounded height. The Bounded Height Conjecture is known to hold. We also present some examples and remarks.

Injective endomorphisms of algebraic and analytic sets

Sławomir Cynk, Kamil Rusek (1991)

Annales Polonici Mathematici

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We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.