Search results for " Projective Space"

Quotients of Hypersurfaces in Weighted Projective Space

2009

Abstract In [Bini, van Geemen, Kelly, Mirror quintics, discrete symmetries and Shioda maps, 2009] some quotients of one-parameter families of Calabi–Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More specifically, let A be an invertible matrix with non-negative integer entries. We introduce varieties XA and in weighted projective space and in , respectively. The variety turns out to be a quotient of a Fermat variety by a finite group. As a by-product, XA is a quotient of a Fermat variety and is a quotient of XA by a finite group. We apply this construction to som…

The isoperimetric inequality and the geodesic spheres. Some geometric consequences

1986

A rigidity theorem for the pair ${\cal q}{\Bbb C} P^n$ (complex hyperquadric, complex projective space)

1999

Given a compact Kahler manifold M of real dimension 2n, let P be either a compact complex hypersurface of M or a compact totally real submanifold of dimension n. Let \(\cal q\) (resp. \({\Bbb R} P^n\)) be the complex hyperquadric (resp. the totally geodesic real projective space) in the complex projective space \({\Bbb C} P^n\) of constant holomorphic sectional curvature 4\( \lambda \). We prove that if the Ricci and some (n-1)-Ricci curvatures of M (and, when P is complex, the mean absolute curvature of P) are bounded from below by some special constants and volume (P) / volume (M) \(\leq \) volume (\(\cal q\))/ volume \(({\Bbb C} P^n)\) (resp. \(\leq \) volume \(({\Bbb R} P^n)\) / volume …

Correction to ?partial spreads in finite projective spaces and partial designs?

1976

On globally generated vector bundles on projective spaces II

2014

Extending a previous result of the authors, we classify globally generated vector bundles on projective spaces with first Chern class equal to three.

Generically split projective homogeneous varieties. II

2012

AbstractThis article gives a complete classification of generically split projective homogeneous varieties. This project was begun in our previous article [PS10], but here we remove all restrictions on the characteristic of the base field, give a new uniform proof that works in all cases and in particular includes the case PGO2n+ which was missing in [PS10].

A characterization of Baer cones in finite projective spaces

1985

On Baer subspaces of finite projective spaces

1983

Maps to Projective Space

2000

One of the main goals of algebraic geometry is to understand the geometry of smooth projective varieties. For instance, given a smooth projective surface X, we can ask a host of questions whose answers might help illuminate its geometry. What kinds of curves does the surface contain? Is it covered by rational curves, that is, curves birationally equivalent to ℙ1? If not, how many rational curves does it contain, and how do they intersect each other? Or is it more natural to think of the surface as a family of elliptic curves (genus-1 Riemann surfaces) or as some other family? Is the surface isomorphic to ℙ2 or some other familiar variety on a dense set? What other surfaces are birationally …

Homological Projective Duality for Determinantal Varieties

2016

In this paper we prove Homological Projective Duality for crepant categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a n x m matrix of linear forms on a given projective space. As applications, we obtain pairs of derived-equivalent Calabi-Yau manifolds, and address a question by A. Bondal asking whether the derived category of any smooth projective variety can be fully faithfully embedded in the derived category of a smooth Fano variety. Moreover we discuss the relation between rationality and categorical representability in codimension two for determinantal varieties.