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Teorema de irreducibilidad para correspondencias algebraicas.

Eugenio Roanes (1980)

Revista Matemática Hispanoamericana

Sea T una correspondencia algebraica irreducible entre dos variedades proyectivas, V y V', sobre un cuerpo k algebraicamente cerrado y de característica cero. Sea W una subvariedad irreducible de V y W' = T{W} la transformada total de W en T. En [1] se estudia el problema de la conexión de W' y en [3] se estudia el problema de la irreducibilidad de la transformada total de W en correspondencias locales. La finalidad de este artículo es la de aprovechar los resultados de los dos trabajos citados,...

The effect of rational maps on polynomial maps

Pierrette Cassou-Noguès (2001)

Annales Polonici Mathematici

We describe the polynomials P ∈ ℂ[x,y] such that P ( 1 / v ⁿ , A ₁ v ⁿ + A ₂ v 2 n + . . . + A m - 1 v n ( m - 1 ) + v n m - k w ) ∈ ℂ [ v , w ] . As applications we give new examples of bad field generators and examples of families of polynomials with smooth and irreducible fibers.

The number of conjugacy classes of elements of the Cremona group of some given finite order

Jérémy Blanc (2007)

Bulletin de la Société Mathématique de France

This note presents the study of the conjugacy classes of elements of some given finite order n in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if n is even, n = 3 or n = 5 , and that it is equal to 3 (respectively 9 ) if n = 9 (respectively if n = 15 ) and to 1 for all remaining odd orders. Some precise representative elements of the classes are given.

The set of points at which a polynomial map is not proper

Zbigniew Jelonek (1993)

Annales Polonici Mathematici

We describe the set of points over which a dominant polynomial map f = ( f 1 , . . . , f n ) : ℂ n → ℂ n is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by ( ∏ i = 1 n d e g f i - μ ( f ) ) / ( m i n i = 1 , . . . , n d e g f i ) .

Towards the classification of weak Fano threefolds with ρ = 2

Joseph Cutrone, Nicholas Marshburn (2013)

Open Mathematics

In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases...

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