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Sia $p : X \to P^{2}$ un fibrato in coniche standard con curva discriminante $Δ$ di grado $d$ . La varietà delle sezioni minime delle superfici $p^{- 1} (C)$ , dove $C$ è una curva di grado $d - 3$ , si spezza in due componenti $C_{+}$ e $C_{-}$ . Si prova che, mediante la mappa di Abel-Jacobi $Φ$ , una di queste componenti domina la Jacobiana intermedia $J X$ , mentre l'altra domina il divisore theta $Θ \subset J X$ . Questi risultati vengono applicati ad alcuni threefold di Fano birazionalmente equivalenti a un fibrato in coniche. In particolare si prova che il generico...

Mixed Automorphic Forms and Invariants of Elliptic Surfaces.

Werner Meyer, Bruce Hunt (1985)

Mathematische Annalen

Mixed Hodge structure of affine hypersurfaces

Hossein Movasati (2007)

Annales de l’institut Fourier

In this article we give an algorithm which produces a basis of the $n$ -th de Rham cohomology of the affine smooth hypersurface $f^{- 1} (t)$ compatible with the mixed Hodge structure, where $f$ is a polynomial in $n + 1$ variables and satisfies a certain regularity condition at infinity (and hence has isolated singularities). As an application we show that the notion of a Hodge cycle in regular fibers of $f$ is given in terms of the vanishing of integrals of certain polynomial $n$ -forms in $ℂ^{n + 1}$ over topological $n$ -cycles on...

Mixed Hodge Structures on the Homotopy of Links.

Alan H. Durfee, Richard Hain (1988)

Mathematische Annalen

Mixed Hodge structures on the intersection cohomology of links

Alan H. Durfee, Morihiko Saito (1990)

Compositio Mathematica

Mixed Hodge theory for unitary local systems.

Klaus Timmerscheidt (1987)

Journal für die reine und angewandte Mathematik

Modules of finite length and $K$ -groups of surface singularities

Marc Levine (1986)

Compositio Mathematica

Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations.

Fabrizio Catanese (1991)

Inventiones mathematicae

Moduli of simple Rank-2 sheaves on K3-surfaces.

Zhenbo Qin (1993)

Manuscripta mathematica

Moduli of stable sheaves on ruled surfaces and their Picard groups.

Zhenbo Qin (1992)

Journal für die reine und angewandte Mathematik

Moduli of Vector Bundles on the Projective Plane.

W. Barth (1977)

Inventiones mathematicae

Modulprobleme in der algebraischen Geometrie III

H.J. FITZNER, M. ROCZEN, G. PFISTER, W. KLEINERT, H. KURKE, Th. ZINK (1978)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Modulräume stabiler 2-Bündel auf Regelflächen.

Heinz Spindler, Hans Jürgen Hoppe (1980)

Mathematische Annalen

Monodromy of a family of hypersurfaces

Vincenzo Di Gennaro, Davide Franco (2009)

Annales scientifiques de l'École Normale Supérieure

Let $Y$ be an $(m + 1)$ -dimensional irreducible smooth complex projective variety embedded in a projective space. Let $Z$ be a closed subscheme of $Y$ , and $δ$ be a positive integer such that $ℐ_{Z, Y} (δ)$ is generated by global sections. Fix an integer $d \geq δ + 1$ , and assume the general divisor $X \in | H^{0} (Y, ℐ_{Z, Y} (d)) |$ is smooth. Denote by $H^{m} {(X; ℚ)}_{⊥ Z}^{van}$ the quotient of $H^{m} (X; ℚ)$ by the cohomology of $Y$ and also by the cycle classes of the irreducible components of dimension $m$ of $Z$ . In the present paper we prove that the monodromy representation on $H^{m} {(X; ℚ)}_{⊥ Z}^{van}$ for the family of smooth...

Monodromy of a family of hypersurfaces containing a given subvariety

Ania Otwinowska, Morihiko Saito (2005)

Annales scientifiques de l'École Normale Supérieure

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