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Effective Criteria for Birational Morphisms
Author(s) -
Hacon Christopher D.
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461070200385x
Subject(s) - morphism , mathematics , birational geometry , pure mathematics , algebraic number , type (biology) , algebraic variety , algebra over a field , mathematical analysis , ecology , biology
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 → 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 ).