An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels.

Henriques, André

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Eric M. Friedlander, Barry Mazur (1994)

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We study certain kinds of geometric correspondences between (possibly singular) algebraic varieties and we obtain comparison results regarding natural filtrations on the homology of varieties.

Foundations of Vietoris homology theory with applications to non-compact spaces

Robert E. Reed

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CONTENTSPreface...................................................................................................................................... 5I. Introduction............................................................................................................................ 7II. Simple chains 2.1. Simplexes............................................................................................................ 12 2.2. Chains..............................................................................................................................

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Robert J. MacG. Dawson (1993)

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An effective Bertini theorem over finite fields.

Ballico, E. (2003)

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Steenrod operations in subanalytic homology

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Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms

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Homology functor in the spirit of the AST is defined, its basic properties are studied. Eilenberg-Steenrod axioms for this functor are formulated and established.

On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles

Fouad Elzein, András Némethi (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $Y$ be a normal crossing divisor in the smooth complex projective algebraic variety $X$ and let $U$ be a tubular neighbourhood of $Y$ in $X$ . Using geometrical properties of different intersections of the irreducible components of $Y$ , and of the embedding $Y \subset X$ , we provide the “normal forms” of a set of geometrical cycles which generate $H_{*} (A, B)$ , where $(A, B)$ is one of the following pairs $(Y, \emptyset)$ , $(X, Y)$ , $(X, X - Y)$ , $(X - Y, \emptyset)$ and $(\partial U, \emptyset)$ . The construction is compatible with the weights in $H_{*} (A, B, ℚ)$ of Deligne’s mixed Hodge structure. The main technical...