منابع مشابه
Free Pencils on Divisors
In algebraic geometry, it is rather typical that the embedding of a variety Y in another varietyX forces strong constraints on the existence of free linear series on Y . For example, a classical result in plane curve theory states that the gonality of a smooth plane curve of degree d is d − 1 ([ACGH]). It is then natural to look for general statements of this flavor. One particular case, which ...
متن کاملA note on companion pencils
Various generalizations of companion matrices to companion pencils are presented. Companion matrices link to monic polynomials, whereas companion pencils do not require monicity of the corresponding polynomial. In the classical companion pencil case (A,B) only the coefficient of the highest degree appears in B’s lower right corner. We will show, however, that all coefficients of the polynomial ...
متن کاملHalphen Pencils on Quartic Threefolds
∼= P, where g(x, y, z) = 0 is a homogeneous equation of the curve Z and (λ, μ) ∈ P. Then a general curve in P is birational to an elliptic curve. Remark 1.1. The construction of pencil P can be generalized to the case when C has at most ordinary double points and the points P1, · · · , P9 are not necessarily distinct (see [3]). The pencil P is called a standard Halphen pencil. Definition 1.2. A...
متن کاملOn Wilkinson's problem for matrix pencils
Suppose that an n-by-n regular matrix pencil A − λB has n distinct eigenvalues. Then determining a defective pencil E−λF which is nearest to A−λB is widely known as Wilkinson’s problem. It is shown that the pencil E − λF can be constructed from eigenvalues and eigenvectors of A − λB when A − λB is unitarily equivalent to a diagonal pencil. Further, in such a case, it is proved that the distance...
متن کاملLefschetz Type Pencils on Contact Manifolds
We define the concept of Lefschetz contact pencil and we show the existence of such structures on any contact manifold. The main idea of the proof is a generalization of the Donaldson arguments used in the symplectic case. We will analyze some of the applications of such existence theorem for the topology of approximately holomorphic contact submanifolds. In particular, we study the topological...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 1875
ISSN: 0024-6115
DOI: 10.1112/plms/s1-7.1.175