The logarithmic Picard group and its tropicalization

Compositio mathematica

article

Samouil Molcho¹  Jonathan Wise² 

[1] ETH Zürich;University of Colorado, Campus Box 395

关键词: logarithmic geometry;    tropical geometry;    Picard group;    Jacobian;    algebraic curves;    14A21;    14C22;    14H40;    14T10;    14C20;    14D20;    14D23;    14H10;    14K30;   

DOI  :  10.1112/S0010437X22007527

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

CC BY