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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
44/2018

Log smoothness and polystability over valuation rings

Karim Adiprasito, Xue Liu, Igor Pak and Michael Temkin

Abstract

Let $\mathcal O$ be a valuation ring of height one of residual characteristic exponent $p$ and with algebraically closed field of fractions. Our main result provides a best possible resolution of the monoidal structure $M_X$ of a log variety $X$ over $\mathcal O$: there exists a log modification $Y\to X$ such that the monoidal structure of $Y$ is polystable. In particular, if $X$ is log smooth over $\mathcal O$ then $Y$ is polystable. As a corollary we deduce that any log variety over $\mathcal O$ possesses a polystable alteration of degreee $p^n$. The core of our proof is a subdivision result for polyhedral complexes satisfying certain rationality conditions.

Received:
Jun 28, 2018
Published:
Jul 18, 2018

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Preprint
2018 Repository Open Access
Karim Adiprasito, Xue Liu, Igor Pak and Michael Temkin

Log smoothness and polystability over valuation rings