Moduli of stable maps in genus one and logarithmic geometry, I
| Autor: | Jonathan Wise, Keli S. Santos-Parker, Dhruv Ranganathan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
quasimaps Space (mathematics) 01 natural sciences elliptic singularities Moduli Interpretation (model theory) logarithmic geometry Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Genus (mathematics) 0103 physical sciences FOS: Mathematics Projective space 0101 mathematics Algebraic Geometry (math.AG) Mathematics 14D23 010102 general mathematics Moduli space Minimal model program Elliptic curve stable maps 010307 mathematical physics Geometry and Topology 14N35 |
| Zdroj: | Geom. Topol. 23, no. 7 (2019), 3315-3366 |
| Popis: | This is the first in a pair of papers developing a framework for the application of logarithmic structures in the study of singular curves of genus $1$. We construct a smooth and proper moduli space dominating the main component of Kontsevich's space of stable genus $1$ maps to projective space. A variation on this theme furnishes a modular interpretation for Vakil and Zinger's famous desingularization of the Kontsevich space of maps in genus $1$. Our methods also lead to smooth and proper moduli spaces of pointed genus $1$ quasimaps to projective space. Finally, we present an application to the log minimal model program for $\mathcal{M}_{1,n}$. We construct explicit factorizations of the rational maps among Smyth's modular compactifications of pointed elliptic curves. Comment: 37 pages, 4 figures. Final version to appear in Geometry & Topology |
| Databáze: | OpenAIRE |
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