Intersection theory of nef b-divisor classes
| Autor: | Dang, Nguyen-Bac, Favre, Charles |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove that any nef b-divisor class on a projective variety defined over an algebraically closed field of characteristic 0 is a decreasing limit of nef Cartier classes. Building on this technical result, we construct an intersection theory of nef b-divisors, and prove several variants of the Hodge index theorem inspired by the work of Dinh and Sibony. We show that any big and basepoint free curve class is a power of a nef b-divisor, and relate this statement to Zariski decompositions of curves classes introduced by Lehmann and Xiao. Our construction allows us to relate various Banach spaces contained in the space of b-divisors which were defined in our previous work.5 Comment: 38 pages. New version: updated references. Our main theorem is now valid over any alg. closed field of char. 0. A section on movable classes was added, but the section on toric b-classes was removed to streamline the discussion |
| Databáze: | arXiv |
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