On certain K-equivalent birational maps

On Certain Groups of Birational Contact Transformations*

Birational Cobordisms and Factorization of Birational Maps

In this paper we develop a Morse-like theory in order to decompose birational maps and morphisms of smooth projective varieties defined over a field of characteristic zero into more elementary steps which are locallyétale isomorphic to equivariant flips, blow-ups and blow-downs of toric varieties (see Theorems 1, 2 and 3). The crucial role in the considerations is played by K *-actions where K ...

Equivalent Birational Embeddings Ii: Divisors

Two divisors in Pn are said to be Cremona equivalent if there is a Cremona modification sending one to the other. We produce infinitely many non equivalent divisorial embeddings of any variety of dimension at most 14. Then we study the special case of plane curves and rational hypersurfaces. For the latter we characterise surfaces Cremona equivalent to a plane, under a mild assumption. Introduc...

Lectures on Factorization of Birational Maps

This is an expanded version of the notes for the lectures given by the author at RIMS in the summer of 1999 to provide a detailed account of the proof for the (weak) factorization theorem of birational maps by Abramovich-Karu-MatsukiW lodarczyk [1]. All the main ideas of these lecture notes, therefore, are derived from the collaboration and joint work with D. Abramovich, K. Karu and J. W lodarc...

On certain equivalent norms on Tsirelson’s space

It remains open an important question as to whether or not there exists a distortable Banach space which is not arbitrarily distortable. The primary candidate for such a space is Tsirelson’s space T . While it is not difficult to directly define, for every 1 < λ < 2, an equivalent norm on T which is a λ-distortion, T does not belong to any general class of Banach spaces known to be arbitrarily ...