Torification and factorization of birational maps

Abramovich, Dan¹ ; Karu, Kalle² ; Matsuki, Kenji³ ; Włodarczyk, Jarosław⁴

¹ Department of Mathematics, Boston University, 111 Cummington Street, Boston, Massachusetts 02215
² Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02139
³ Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana 47907-1395
⁴ Instytut Matematyki UW, Banacha 2, 02-097 Warszawa, Poland

Journal of the American Mathematical Society, Tome 15 (2002) no. 3, pp. 531-572

Résumé

Building on work of the fourth author and Morelli’s work, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field $K$ of characteristic zero is a composite of blowings up and blowings down with nonsingular centers.

Détail

DOI : 10.1090/S0894-0347-02-00396-X

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