Nonarchimedean geometry, tropicalization, and metrics on curves
Publication
, Journal Article
Baker, M; Payne, S; Rabinoff, J
Published in: Algebraic Geometry
January 1, 2016
We develop a number of general techniques for comparing analytifications and tropicalizations of algebraic varieties. Our basic results include a projection formula for tropical multiplicities and a generalization of the Sturmfels-Tevelev multiplicity formula in tropical elimination theory to the case of a nontrivial valuation. For curves, we explore in detail the relationship between skeletal metrics and lattice lengths on tropicalizations and show that the maps from the analytification of a curve to the tropicalizations of its toric embeddings stabilize to isometries on finite subgraphs. Other applications include generalizations of Speyer's well-spacedness condition and the Katz- Markwig-Markwig results on tropical j-invariants.
Duke Scholars
Published In
Algebraic Geometry
DOI
EISSN
2214-2584
ISSN
2313-1691
Publication Date
January 1, 2016
Volume
3
Issue
1
Start / End Page
63 / 105
Citation
APA
Chicago
ICMJE
MLA
NLM
Baker, M., Payne, S., & Rabinoff, J. (2016). Nonarchimedean geometry, tropicalization, and metrics on curves. Algebraic Geometry, 3(1), 63–105. https://doi.org/10.14231/AG-2016-004
Baker, M., S. Payne, and J. Rabinoff. “Nonarchimedean geometry, tropicalization, and metrics on curves.” Algebraic Geometry 3, no. 1 (January 1, 2016): 63–105. https://doi.org/10.14231/AG-2016-004.
Baker M, Payne S, Rabinoff J. Nonarchimedean geometry, tropicalization, and metrics on curves. Algebraic Geometry. 2016 Jan 1;3(1):63–105.
Baker, M., et al. “Nonarchimedean geometry, tropicalization, and metrics on curves.” Algebraic Geometry, vol. 3, no. 1, Jan. 2016, pp. 63–105. Scopus, doi:10.14231/AG-2016-004.
Baker M, Payne S, Rabinoff J. Nonarchimedean geometry, tropicalization, and metrics on curves. Algebraic Geometry. 2016 Jan 1;3(1):63–105.
Published In
Algebraic Geometry
DOI
EISSN
2214-2584
ISSN
2313-1691
Publication Date
January 1, 2016
Volume
3
Issue
1
Start / End Page
63 / 105