منابع مشابه
On submaximal plane curves
We prove that a submaximal curve in P has sequence of multiplicities (μ, ν, . . . , ν), with μ < sν for every integer s with (s− 1)(s+ 2) ≥ 6.76( r − 1). This note is a sequel to [10], where a specialization method was developed in order to bound the degree of singular plane curves. The problem under consideration is, given a system of multiplicities (m) = (m1,m2, . . . ,mr) ∈ Z and points p1, ...
متن کاملOn the Nagata Problem
In the course of his construction [N] of a counterexample to Hilbert's 14th problem, Nagata was led to formulate a conjectural lower bound on the degree of a plane curve having assigned multiplicities at a generic collection of points. To state the conjecture precisely, recall first that the multiplicity mult P (C) of an arbitrary plane curve C (=pos
متن کاملDeligne’s Notes on Nagata Compactifications
We provide a proof of Nagata’s compactification theorem: any separated map of finite type between quasi-compact and quasi-separated schemes (e.g., noetherian schemes) factors as an open immersion followed by a proper morphism. This is a detailed exposition of private notes of Deligne that translate Nagata’s method into modern terms, and includes some applications of general interest in the theo...
متن کاملTwistor Lines on Nagata Threefold
We present an explicit description of twistor lines in M. Nagata’s example of nonprojective complete algebraic variety and give a direct proof of the fact that Nagata’s example is a compactification of the twistor space of a hyperKähler metric on the cotangent bundle of P . We particularly observe that there exists a pair of 4-dimensional families of real lines and that precisely one of these f...
متن کاملThe Nagata automorphism is wild.
It is proved that the well known Nagata automorphism of the polynomial ring in three variables over a field of characteristic zero is wild, that is, it can not be decomposed into a product of elementary automorphisms.
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2003
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap80-0-20