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A new proof of desingularization over fields of characteristic zero.

Santiago Encinas, Orlando Villamayor (2003)

Revista Matemática Iberoamericana

We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness (see also [171 page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka 's procedure. This is done by showing that desingularization...

A nonlinearizable action of S 3 on 4

Gene Freudenburg, Lucy Moser-Jauslin (2002)

Annales de l’institut Fourier

The main purpose of this article is to give an explicit algebraic action of the group S 3 of permutations of 3 elements on affine four-dimensional complex space which is not conjugate to a linear action.

A note on 2-dimensional arithmetic symbols on Gl(n, ΣS).

Fernando Pablos Romo (2007)

Publicacions Matemàtiques

The aim of this note is to offer a summary of the definitions and properties of arithmetic symbols on the linear group Gl(n, F) -F being an arbitrary discrete valuation field- and to show that the natural generalizations of the Parshin symbol on an algebraic surface S to the linear group Gl(n, ΣS) do not allow us to define new 2-dimensional symbols on S.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

A note on a theorem of Horikawa.

Francesco Zucconi (1997)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we classify the algebraic surfaces on C with KS2=4, pg=3 and canonical map of degree d=3. By our result and the previous one of Horikawa (1979) we obtain the complete determination of surfaces with K2=4 and pg=3.

A Note on a Theorem of Lion

Zofia Ambroży (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

In this note we bind together Wilkie's complement theorem with Lion's theorem on geometric, regular and 0-regular families of functions.

A note on a theorem of Xiao Gang.

Margarita Mendes Lopes (2004)

Collectanea Mathematica

In 1985 Xiao Gang proved that the bicanonical surface of a complex surface S of general type with p2(S) > 2 is not composed of a pencil. In this note a new proof of this theorem is presented.

A note on Bézout's theorem

Sławomir Rams, Piotr Tworzewski, Tadeusz Winiarski (2005)

Annales Polonici Mathematici

We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.

A note on Bierstone-Milman-Pawłucki's paper "Composite differentiable functions"

Krzysztof Jan Nowak (2011)

Annales Polonici Mathematici

We demonstrate that the composite function theorems of Bierstone-Milman-Pawłucki and of Glaeser carry over to any polynomially bounded, o-minimal structure which admits smooth cell decomposition. Moreover, the assumptions of the o-minimal versions can be considerably relaxed compared with the classical analytic ones.

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