arXiv 1407.26292014-07math.AG

可对角化群作用在环面格式上的Torification

Torification of diagonalizable group actions on toroidal schemes

Dan Abramovich, Michael Temkin

备注：: The statement of the main result was again strengthened to accommodate our work on functorial factorization of birational maps: we now blow up an ideal without need to further normalize, using results in the new section 5. Some errors were corrected, in particular we made the functorial choice of a torific ideal more precise

摘要：

本文研究了可对角化群在环形格式（即代数正则对数格式）上的作用。特别是，我们表明，所谓的环形行动的商再次是一个环形计划。我们的主要结果构造了一个任意行动的一个典型torification -使行动toridal后，一个等变的爆破。这在各个方面推广了Abramovich-de Jong，Abramovich-Karu-Matsuki-Wavodarczyk和Gabber的早期结果。

英文摘要：

We study actions of diagonalizable groups on toroidal schemes (i.e. logarithmically regular logarithmic schemes). In particular, we show that for so-called toroidal actions the quotient is again a toroidal scheme. Our main result constructs for an arbitrary action a canonical torification - making the action toridal after an equivariant blowings up. This extends earlier results of Abramovich-de Jong, Abramovich-Karu-Matsuki-Włodarczyk, and Gabber in various aspects.

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