Pure and Applied Mathematics Quarterly
Volume 16 (2020)
Special Issue in Honor of Yuri Manin: Part 3 of 3
Guest Editors: Lizhen Ji, Kefeng Liu, Yuri Tschinkel, and Shing-Tung Yau
Pages: 35 – 124
For a complete algebraic space with a nef quasipolarization and its closed subspace which includes the exceptional locus of the quasipolarization, the paper establishes the existence of an infinitesimal neighborhood of the subspace such that for any quasipolarized morphism of the neighborhood into a polarized scheme there exists a quasipolarized modification of the space into a polarized scheme. This is a quasipolarized version of the wellknown Artin modification. As applications nonprojective versions of the semiampleness criterion of Birkar in general and of Keel in positive characteristics are obtained.
Partially supported by NSF grant DMS-1400943.
Received 12 June 2017
Published 6 February 2020