Specialization of linear systems from curves to graphs
By Matthew Baker. 2007
269 citations recorded by the source corpus.
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and tropical geometry.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/664423ca62fcf92a0819b7eeeecfaf8d19d25315
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Matthew Baker
- David Jensen
- Omid Amini
- Lucia Caporaso
- Joseph Rabinoff
- Dhruv Ranganathan
- Erwan Brugallé
- Christian Haase
In Computational Theory and Mathematics
- Matthew Baker
- David Jensen
- Omid Amini
- Dhruv Ranganathan
- Lucia Caporaso
- Joseph Rabinoff
- Erwan Brugallé
- Christian Haase
In Geometry and Topology
- David Jensen
- Matthew Baker
- Omid Amini
- Dhruv Ranganathan
- Lucia Caporaso
- Joseph Rabinoff
- Erwan Brugallé
- Josephine Yu
Citations in the corpus
- Linear systems on tropical curves (2009, background): “Example 29 (Circle, degree 3 divisor) Let be a circle of circumference 3, identified with R/3Z and let D be the degree 3 divisor [0]+[1]+[2].”
- Degeneration of Linear Series from the Tropical Point of View and Applications (2015, methodology): “2 for discretely valued fields, proved using deformation theory, can be found in Appendix B of [Bak08b].”
- Brill-Noether theory for curves of a fixed gonality (2017, background): “The upper bound follows from Baker’s specialisation lemma [8].”
- Lifting harmonic morphisms II: tropical curves and metrized complexes (2014, background): “MR 3046301 Zbl 1284.14087 [Baker 2008] M. Baker, “Specialization of linear systems from curves to graphs”, Algebra Number Theory 2:6 (2008), 613–653.”
- Riemann–Roch theory for weighted graphs and tropical curves (2011, methodology): “of loops adjacent to vi in G). Now replace Gby G′ and use exactly the same proof. (Alternatively, one could apply the same argument used in [C3, Prop. 5.5], where the original Specialization Lemma of [B] was extended to weightless graphs admitting loops.) 5. Riemann-Roch on weighted tropical curves ”
- Linear series on metrized complexes of algebraic curves (2012, methodology): “As mentioned above, the specialization theory from [7] works best in the case where the family is maximally degenerate; in other cases, the dual graph of the family forgets too much information.”