On the concavity of the arithmetic volumes

Abstract

In this note, we study the differentiability of the arithmetic volumes along arithmetic R-divisors, and give some equality conditions for the Brunn-Minkowski inequality for arithmetic volumes over the cone of nef and big arithmetic R-divisors.

35 pages

References in corpus (3)

• Toward Dirichlet's unit theorem on arithmetic varieties
• The arithmetic Hodge index theorem for adelic line bundles II
• Teissier's problem on inequalities of nef divisors over an arbitrary field

Cited by in corpus (1)

• A numerical characterization of nef adelic divisors