Birational geometry of foliations by Marco Brunella

By Marco Brunella

The textual content provides the birational class of holomorphic foliations of surfaces.  It discusses at size the idea constructed by means of L.G. Mendes, M. McQuillan and the writer to check foliations of surfaces  within the spirit of the category of complicated algebraic surfaces.

Show description

Read Online or Download Birational geometry of foliations PDF

Best number theory books

Number Theory 1: Fermat's Dream

This can be the English translation of the unique eastern ebook. during this quantity, "Fermat's Dream", center theories in glossy quantity concept are brought. advancements are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the quantity fields. This paintings offers a chic standpoint at the ask yourself of numbers.

Initial-Boundary Value Problems and the Navier-Stokes Equations

This e-book offers an advent to the tremendous topic of preliminary and initial-boundary worth difficulties for PDEs, with an emphasis on purposes to parabolic and hyperbolic structures. The Navier-Stokes equations for compressible and incompressible flows are taken for instance to demonstrate the consequences.

Additional info for Birational geometry of foliations

Example text

T. Brown [1971] gave a survey on constructing strongly nonrepetitive sequences. Entringer, Jackson, and Schatz [1974] proved that every infinite word over a 2-letter alphabet contains arbitrarily long abelian squares. Ker¨anen [1992] solved Erd˝os’s problem by exhibiting a strongly nonrepetitive sequence over a 4-letter alphabet. Carpi [1998] showed that there are uncountably many abelian squarefree words over a 4-letter alphabet, and that the number of abelian squarefree words of each length grows exponentially.

Mignosi and Pirillo [1992] proved√that the critical exponent for the Fibonacci . 618. For other results on critical 2 exponents, see Klepinin and Sukhanov [1999], Vandeth [2000], and Damanik and Lenz [2002]. Erd˝os [1961, p. 240] first raised the problem of the existence of infinite abelian squarefree words. ) Evdokimov [1968] constructed such a sequence on 25 symbols. Pleasants [1970] improved this to 5 symbols. T. Brown [1971] gave a survey on constructing strongly nonrepetitive sequences. Entringer, Jackson, and Schatz [1974] proved that every infinite word over a 2-letter alphabet contains arbitrarily long abelian squares.

1 The critical exponent of the Thue–Morse word t is 2. Proof. The word t begins 011 · · · and hence contains a square. If t contained a (2 + )-power for any > 0, then it would contain an overlap. 1. There also exist various generalizations of squarefreeness. We say a word is an abelian square if it is of the form w w where w is a permutation of w. A word is abelian squarefree if it contains no abelian squares. 11) for more information. Another generalization is to study more general pattern avoidance problems.

Download PDF sample

Rated 4.05 of 5 – based on 7 votes