On Singular Projective Deformations of Two Second Class Totally Focal Pseudocongruences of Planes
نویسنده
چکیده
Let C: L L be a projective deformation of the second order of two totally pn focal pseudocongruences L and L of (m-l)-planes in projective spaces and n, 2m-i < n < 3m-l, and let K be a collineation realizing such a C. The deformation C is said to be weakly singular, singular, or a-strongly singular, s 3,4,..., if the collineation K gives projective deformations of order i, 2 or of all corresponding focal surfaces of L and L. It is proved that C is weakly singular and conditions are found for C to be singular. The pseudocongruences L and L are identical if and only f C is 3-strongly singular.
منابع مشابه
Constructing Low Degree Hyperbolic Surfaces In
We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a " hyperbolic non-percolation " property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbol...
متن کاملConstructing Low Degree Hyperbolic Surfaces in P
We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a “hyperbolic non-percolation” property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbolic...
متن کاملCanonical singular hermitian metrics on relative canonical bundles
We introduce a new class of canonical AZD’s (called the supercanonical AZD’s) on the canonical bundles of smooth projective varieties with pseudoeffective canonical classes. We study the variation of the supercanonical AZD ĥcan under projective deformations and give a new proof of the invariance of plurigenera. This paper is a continuation of [Ts5]. MSC: 14J15,14J40, 32J18
متن کاملCracked piezoelectric layer bounded between two orthotropic half-planes
This paper deals with the behavior of anti-plane shear crack in a piezoelectric layer bounded between two orthotropic half-planes within the framework of linear electroelasticity. The crack surfaces are assumed to be permeable or impermeable. The analysis is based on the stress fields caused by Volterra-type screw dislocation in the medium. Fourier transforms are used to reduce the dislocation ...
متن کاملSpreads , Translation Planes and Kerdock Sets
In an orthogonal vector space of type l)/(4n, q), a spread is a family of q2n-l+ totally singular 2n-spaces which induces a partition of the singular points; these spreads are closely related to Kerdock sets. In a 2m-dimensional vector space over GF(q), a spread is a family of q + subspaces of dimension m which induces a partition of the points of the underlying projective space; these spreads ...
متن کامل