A Poincaré duality type theorem for polyhedra

Gerald Leonard Gordon

Displaying similar documents to “A Poincaré duality type theorem for polyhedra”

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...

The modified diagonal cycle on the triple product of a pointed curve

Benedict H. Gross, Chad Schoen (1995)

Annales de l'institut Fourier

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Let $X$ be a curve over a field $k$ with a rational point $e$ . We define a canonical cycle $Δ_{e} \in Z^{2} (X^{3})_{hom}$ . Suppose that $k$ is a number field and that $X$ has semi-stable reduction over the integers of $k$ with fiber components non-singular. We construct a regular model of $X^{3}$ and show that the height pairing $⟨ τ_{*} (Δ_{e}), τ_{*}^{'} (Δ_{e}) ⟩$ is well defined where $τ$ and $τ^{'}$ are correspondences. The paper ends with a brief discussion of heights and $L$ -functions in the case that $X$ is a modular curve.

On signatures associated with ramified coverings and embedding problems

J. Wood, Emery Thomas (1973)

Annales de l'institut Fourier

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Given a cohomology class $ξ \in H^{2} (M; Z)$ there is a smooth submanifold $K \subset M$ Poincaré dual to $ξ$ . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in $C P_{n}$ . This note summarizes some results on the question: how does the divisibility of $ξ$ restrict the dual submanifolds $K$ in this class ? A formula for signatures associated with a $d$ -fold ramified cover of $M$ branched along $K$ is given and a proof is included in case $d = 2$ .

On resolving singularities and relating bordism to homology

S. Buoncristiano, M. Dedò (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Levi's forms of higher codimensional submanifolds

Andrea D&#039;Agnolo, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $X ≅ C^{n}$ , let $M$ be a $C^{2}$ hypersurface of $X$ , $S$ be a $C^{2}$ submanifold of $M$ . Denote by $L_{M}$ the Levi form of $M$ at $z_{0} \in S$ . In a previous paper [3] two numbers $s^{\pm} (S, p)$ , $p \in {({\dot{T}}_{S}^{*} X)}_{z_{0}}$ are defined; for $S = M$ they are the numbers of positive and negative eigenvalues for $L_{M}$ . For $S \subset M$ , $p \in S \times_{M} \dot{T}^{*}_{S} X)$ , we show here that $s^{\pm} (S, p)$ are still the numbers of positive and negative eigenvalues for $L_{M}$ when restricted to $T_{z_{0}}^{C} S$ . Applications to the concentration in degree for microfunctions at the boundary are given.