Erratum to “The Hölder continuous subsolution theorem for complex Hessian equations”

Benali, Amel; Zériahi, Ahmed

doi:10.5802/jep.157

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2022

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“…One might also want to generalize Theorem C and try to solve the equation where and are fixed and lie in an appropriate subspace of numerical divisor -classes. This would be analogous to solving mixed Monge–Ampere equations in the complex domain (see [DK14, LN15, BZ20, BZ21] and the references therein for recent developments on this problem).…”

Section: Introductionmentioning

confidence: 99%

Intersection theory of nefb-divisor classes

Dang¹,

Favre²

2022

Compositio Math.

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We prove that any nef $b$ -divisor class on a projective variety defined over an algebraically closed field of characteristic zero 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 the Zariski decomposition 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.

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