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EFFECTIVE CRITERIA FOR BIRATIONAL MORPHISMS

Published online by Cambridge University Press:  24 March 2003

CHRISTOPHER D. HACON
CHRISTOPHER D. HACON
Affiliation:
Department of Mathematics, 2nd Floor, Surge Building, University of California, Riverside, CA 92521-0135, [email protected] Current address: Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, Utah 84112-0090 USA
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Abstract

The purpose of the paper is to illustrate how vanishing theorems can be used to give effective criteria for a generically finite morphism $f\,{:}\,X\,{\longrightarrow}\,Y$ of smooth complex projective algebraic varieties to be birational. In particular, as a consequence of a non-vanishing theorem of Kollár, it is shown that if $Y$ is of general type and has generically large algebraic fundamental group, then $f$ is birational if and only if $P_2(X)\,{=}\,P_2(Y)$.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 337 - 348
Copyright
The London Mathematical Society 2003

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