Burgos Gil, Jose Ignacio and Gubler, Walter and Jell, Philipp and Kuennemann, Klaus and Martin, Florent and Lazarsfeld, Robert (2020) Differentiability of non-archimedean volumes and non-archimedean Monge-Ampere equations. ALGEBRAIC GEOMETRY, 7 (2). pp. 113-152. ISSN 2313-1691, 2214-2584
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Let X be a normal projective variety over a complete discretely valued field and L a line bundle on X. We denote by X-an the analytification of X in the sense of Berkovich and equip the analytification L-an of L with a continuous metric parallel to parallel to. We study non-archimedean volumes, a tool which allows us to control the asymptotic growth of small sections of big powers of L. We prove that the non-archimedean volume is differentiable at a continuous semipositive metric and that the derivative is given by integration with respect to a Monge-Ampere measure. Such a differentiability formula had been proposed by M. Kontsevich and Y. Tschinkel. In residue characteristic zero, it implies an orthogonality property for non-archimedean plurisubharmonic functions which allows us to drop an algebraicity assumption in a theorem of S. Boucksom, C. Favre and M. Jonsson about the solution to the non-archimedean Monge-Ampere equation. The appendix by R. Lazarsfeld establishes the holomorphic Morse inequalities in arbitrary characteristic.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LINE BUNDLES; THEOREM; non-archimedean geometry; Monge-Ampere equation; volumes of line bundles |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Klaus Künnemann Mathematics > Prof. Dr. Walter Gubler |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Mar 2021 08:17 |
| Last Modified: | 30 Mar 2021 08:17 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45056 |
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