Variations on Log Sarkisov Program for Surfaces

Details Variations on Log Sarkisov Program for Surfaces Variations on Log Sarkisov Program for Surfaces

2008-02-18

arxiv.org/abs/0802.2441v2

Mathematics

Algebraic Geometry

Revised and enlarged version with new examples and applications

Scientific paper

Let (S, BS) be the log-pair associated with a compactification of a given smooth quasi-projective surface V . Under the assumption that the boundary BS is irreducible, we propose an algorithm, in the spirit of the (log) Sarkisov program, to factorize any automorphism of V into a sequence of elementary links in the framework of the logarithmic Mori theory. The new noteworthy feature of our algorithm is that all the blow-ups and contractions involved in the process occur on the boundary.

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