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math.AG2025
Positive geometries and canonical forms via mixed Hodge theory
Francis Brown, Clément Dupont
''Positive geometries'' are a class of semi-algebraic domains which admit a unique ''canonical form'': a logarithmic form whose residues match the boundary structure of the domain.…
math.AG2024
Logarithmic morphisms, tangential basepoints, and little disks
Clément Dupont, Erik Panzer, Brent Pym
We develop the theory of "virtual morphisms" in logarithmic algebraic geometry, introduced by Howell. It allows one to give algebro-geometric meaning to various useful maps of topo…
math.AG2024
An introduction to mixed Tate motives
Clément Dupont
Mixed Tate motives are central objects in the study of cohomology groups of algebraic varieties and their arithmetic invariants. They also play a crucial role in a wide variety of…