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compactification of C2 — 1 results found.

      
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Compactifications of $\mathbb{C}^2$ via pencils of jets of curves
C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (3) 2012, pp. 79–96
Pinaki Mondal (Received: 2011/11/21)

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This article is mainly an announcement of some of the results in the articles Primitive normal compactifications of the affine plane I and II where we study normal compactifications of the affine plane from the point of view of associated pencils of jets of curves and corresponding valuations on the field of rational functions. We find an explicit criterion to determine if a discrete valuation corresponds to a normal compactification of \(\mathbb{C}^2\) which is primitive (i.e., the curve at infinity is irreducible). We show that a primitive normal compactification of \(\mathbb{C}^2\) is projective iff it is algebraic iff the associated pencil of jets of curves has a representative which has only one place at infinity. As an application we compute the moduli space of primitive projective compactifications of \(\mathbb{C}^2\). We also characterize primitive normal compactifications of \(\mathbb{C}^2\) which are not algebraic.

Cet article est principalement une annonce de certains résultats dans les articles Primitive compactifications normales du plan affine I et II où l’on étudie les compactifications normales du plan affine du point de vue des pinceaux associés avec les jets de courbes et des valuations correspondant sur le corps des fonctions rationnelles. Nous trouvons un critère explicite pour déterminer si une valuation discrète corresponde à une compactification normale de \(\mathbb{C}^2\) qui est primitifs (i.e., la courbe à l’infini est irréductible). Nous montrons qu’une compactification normale primitive de \(\mathbb{C}^2\) est projectif si et seulement si elle est algébrique si et seulement si le pinceau associé de jets de courbes a un représentant qui n’a qu’un seul endroit à l’infini. Comme application nous calculons l’espace des modules des compactifications primitive projectif de \(\mathbb{C}^2\). Nous avons également caractérisé les primitives compactifications normal de \(\mathbb{C}^2\) qui ne sont pas algébriques.

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

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