On the number and boundedness of log minimal models of general type
| Autor: | Diletta Martinelli, Stefan Schreieder, Luca Tasin |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
primary 14E30
32Q55 secondary 14D99 14J30 Betti number General Mathematics 010102 general mathematics Dimension (graph theory) Minimal models Type (model theory) 01 natural sciences Volume form Combinatorics Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Bounded function 0103 physical sciences FOS: Mathematics Canonical model 010307 mathematical physics 0101 mathematics Algebraic Geometry (math.AG) Projective variety Mathematics |
| Zdroj: | Martinelli, D, Schreieder, S & Tasin, L 2020, ' On the number and boundedness of log minimal models of general type ', Annales Scientifiques de l'École Normale Supérieure, vol. 53, pp. 1183-1207 . https://doi.org/10.24033/asens.2443 |
| ISSN: | 1873-2151 0012-9593 |
| DOI: | 10.24033/asens.2443 |
| Popis: | We show that the number of marked minimal models of an n-dimensional smooth complex projective variety of general type can be bounded in terms of its volume, and, if n=3, also in terms of its Betti numbers. For an n-dimensional projective klt pair (X,D) with $K_X+D$ big, we show more generally that the number of its weak log canonical models can be bounded in terms of the coefficients of D and the volume of $K_X+D$. We further show that all n-dimensional projective klt pairs (X,D), such that $K_X+D$ is big and nef of fixed volume and such that the coefficients of D are contained in a given DCC set, form a bounded family. It follows that in any dimension, minimal models of general type and bounded volume form a bounded family. 27 pages; final version; to appear in Annales scientifiques de l'ENS |
| Databáze: | OpenAIRE |
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