2014/08/31 by Dan Abramovich, Qile Chen, Steffen Marcus +1 · 2 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Algebraic number #Logarithm #Moduli of algebraic curves #Moduli space #Polynomial and algebraic computation #Scheme (mathematics) #Space (punctuation) #Stack (abstract data type) #Tensor decomposition and applications #math.AG
paper · pdf · doi:10.4171/jems/728
published as Journal of the European Mathematical Society, Volume 19, Issue 9 (2017). 2783-2809 · 32 pages, 2 figures. v3: Significant changes. Final version appears in the Journal of the European Mathematical Society
openalex created_date 2016/06/24 · openalex publication_date 2017/08/07 · arxiv created 2021/01/22 · arxiv updated 2021/01/25 · openalex updated_date 2026/08/05
We prove that the moduli space of stable logarithmic maps from logarithmic curves to a fixed target logarithmic scheme is a proper algebraic stack when the target scheme is projective with fine and saturated logarithmic structure. This was previously known only with further restrictions on the logarithmic structure of the target.