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      Torification of diagonalizable group actions on toroidal schemes

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          Abstract

          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 an equivariant blowings up. This extends earlier results of Abramovich-de Jong, Abramovich-Karu-Matsuki-W{\l}odarczyk, and Gabber in various aspects.

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          Author and article information

          Journal
          2014-07-09
          2015-12-27
          Article
          1407.2629
          beffb4d8-568a-4b31-8105-3e1b554c740c

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          14L30, 14A15, 14E05
          The statement of Theorem 1.1.3 was slightly strengthened (as required by our forthcoming work on factorization of birational maps for qe schemes)
          math.AG

          Geometry & Topology
          Geometry & Topology

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