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Displaying 21 – 40 of 69

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Frédéric Campana, Thomas Peternell (2011)

Bulletin de la Société Mathématique de France

We first prove a strengthening of Miyaoka’s generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold $X$ have a pseudo-effective (instead of generically nef) determinant. A first consequence is that $X$ is of general type if its cotangent bundle contains a subsheaf with ‘big’ determinant. Among other applications, we deduce that if the universal cover of $X$ is not covered by compact positive-dimensional analytic subsets,...

Graded Betti numbers of some embedded rational n-folds.

A.V. Geramita, A. Gimigliano (1995)

Mathematische Annalen

Group law on the intersection of two quadrics

Ron Donagi (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Higher-Dimensional Analogues of Inoue-Hirzebruch Surfaces.

G.K. Sankaran (1986)

Mathematische Annalen

Hilbert schemes of hypersurfaces and numerical criterions.

Bjorn Adlandsvik (1985)

Mathematica Scandinavica

Irregularity fo certain algebraic fiber spaces.

Jin-Xing Chai (1998)

Manuscripta mathematica

Kähler manifolds with numerically effective Ricci class

Jean-Pierre Demailly, Thomas Peternell, Michael Schneider (1993)

Compositio Mathematica

Koszul cohomology and $k$ -normality of a projective variety.

Alzati, A., Besana, G.M. (2000)

Beiträge zur Algebra und Geometrie

Lagrangian fibrations on generalized Kummer varieties

Martin G. Gulbrandsen (2007)

Bulletin de la Société Mathématique de France

We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface $A$ of Picard number one we find the following: The Kummer variety $K^{n} A$ is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if $n$ is a perfect square. And this is the case if and only if $K^{n} A$ carries a divisor with vanishing Beauville-Bogomolov square.

Minimal models and the Kodaira dimension of algebraic fiber spaces.

Yujiro Kawamata (1985)

Journal für die reine und angewandte Mathematik

Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected

Apostol Apostolov (2014)

Annales de l’institut Fourier

We show that the moduli space of polarized irreducible symplectic manifolds of $K 3^{[n]}$ -type, of fixed polarization type, is not always connected. This can be derived as a consequence of Eyal Markman’s characterization of polarized parallel-transport operators of $K 3^{[n]}$ -type.

Morphisms of projective varieties from the viewpoint of minimal model theory [Book]

Marco Andreatta, Massimiliano Mella (2003)

Natural $G$ -constellation families.

Logvinenko, Timothy (2008)

Documenta Mathematica

On a characterization of an abelian variety in the classification theory of algebraic varieties

Yujiro Kawamata, Eckart Viehweg (1980)

Compositio Mathematica

On degenerate secant varieties of secant defect two.

Masahiro Ohno (1997)

Manuscripta mathematica

On extremal rays of the higher dimensional varieties.

Tetsuya Ando (1985)

Inventiones mathematicae

On Kähler-Einstein metrics on certain Kahler manifolds with C1 (M) > 0.

G. Tian (1987)

Inventiones mathematicae

On projective toric varieties whose defining ideals have minimal generators of the highest degree

Shoetsu Ogata (2003)

Annales de l'Institut Fourier

It is known that generators of ideals defining projective toric varieties of dimension $n$ embedded by global sections of normally generated line bundles have degree at most $n + 1$ . We characterize projective toric varieties of dimension $n$ whose defining ideals must have elements of degree $n + 1$ as generators.

On some special Fano manifolds.

Lanteri, Antonio, Sacchi, Cristiana S. (1996)

Beiträge zur Algebra und Geometrie

On the adjunction theoretic classification of polarized varieties.

A.J. Sommese, M.C. Beltrametti (1992)

Journal für die reine und angewandte Mathematik

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