We construct the logarithmic and tropical Picard groups of a family of logarithmic curves and realize the latter as the quotient of the former by the algebraic Jacobian. We show that the logarithmic Jacobian is a proper family of logarithmic abelian varieties over the moduli space of Deligne-Mumford stable curves, but does not possess an underlying algebraic stack. However, the logarithmic Picard group does have logarithmic modifications that are representable by logarithmic schemes, all of which are obtained by pullback from subdivisions of the tropical Picard group.

The Logarithmic Picard group and its Tropicalization / Molcho, S; Wise, J. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - (2022). [10.1112/S0010437X22007527]

The Logarithmic Picard group and its Tropicalization

Molcho S;
2022

Abstract

We construct the logarithmic and tropical Picard groups of a family of logarithmic curves and realize the latter as the quotient of the former by the algebraic Jacobian. We show that the logarithmic Jacobian is a proper family of logarithmic abelian varieties over the moduli space of Deligne-Mumford stable curves, but does not possess an underlying algebraic stack. However, the logarithmic Picard group does have logarithmic modifications that are representable by logarithmic schemes, all of which are obtained by pullback from subdivisions of the tropical Picard group.
2022
algebraic curves; Jacobian; logarithmic geometry; Picard group; tropical geometry
01 Pubblicazione su rivista::01a Articolo in rivista
The Logarithmic Picard group and its Tropicalization / Molcho, S; Wise, J. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - (2022). [10.1112/S0010437X22007527]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1719456
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