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math.AG2022
The arithmetic volume of hypersurfaces in toric varieties and Mahler measures
Mounir Hajli
In this paper we determine the canonical arithmetic volume of hypersurfaces in smooth projective toric varieties. As a consequence, we prove a generalized Hodge index theorem on hy…
math.AG2022
The theta invariants and the volume function on arithmetic varieties
Mounir Hajli
We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to t…