Bounded Volume Denominators and Bounded Negativity
| Autor: | Matthias Nickel, Alex Küronya, Thomas Bauer, Brian Harbourne |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics Negativity effect 01 natural sciences 010101 applied mathematics Mathematics - Algebraic Geometry Arbitrarily large 14A25 14C20 Bounded function Turn (geometry) Line (geometry) FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) Volume (compression) Mathematics |
| Zdroj: | International Mathematics Research Notices. 2021:18476-18488 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnz335 |
| Popis: | In this paper, we study the question of whether on smooth projective surfaces the denominators in the volumes of big line bundles are bounded. In particular, we investigate how this condition is related to bounded negativity (i.e., the boundedness of self-intersections of irreducible curves). Our 1st result shows that boundedness of volume denominators is equivalent to primitive bounded negativity, which in turn is implied by bounded negativity. We connect this result to the study of semi-effective orders of divisors: our 2nd result shows that negative classes exist, which become effective only after taking an arbitrarily large multiple. |
| Databáze: | OpenAIRE |
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