Skip to content

Research at St Andrews

Lifting tropical self intersections

Research output: Contribution to journalArticlepeer-review

Author(s)

Yoav Len, Matt Satriano

School/Research organisations

Abstract

We study the tropicalization of intersections of plane curves, under the assumption that they have the same tropicalization. We show that the set of tropical divisors that arise in this manner is a pure dimensional balanced polyhedral complex and compute its dimension. When the genus is at most 1, we show that all the tropical divisors that move in the expected dimension are realizable. As part of the proof, we introduce a combinatorial tool for explicitly constructing large families of realizable tropical divisors.

Close

Details

Original languageEnglish
Article number105138
Number of pages21
JournalJournal of Combinatorial Theory, Series A
Volume170
Early online date4 Oct 2019
DOIs
Publication statusPublished - Feb 2020

    Research areas

  • Tropical geometry, Intersection theory, Divisor theory, Chip-firing, Polyhedral complexes, Elliptic curves

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Prym-Brill-Noether loci of special curves

    Creech, S., Len, Y., Ritter, C. & Wu, D., 25 Aug 2020, In: International Mathematics Research Notices. Advance Articles, 41 p.

    Research output: Contribution to journalArticlepeer-review

  2. Lifting tropical bitangents

    Len, Y. & Markwig, H., Jan 2020, In: Journal of Symbolic Computation. 96, p. 122-152

    Research output: Contribution to journalArticlepeer-review

  3. Projective duals to algebraic and tropical hypersurfaces

    Ilten, N. & Len, Y., Nov 2019, In: Proceedings of the London Mathematical Society. 119, 5, p. 1234-1278

    Research output: Contribution to journalArticlepeer-review

  4. Bitangents of non-smooth tropical quartics

    Lee, H. & Len, Y., 5 Jul 2018, In: Portugaliae Mathematica. 75, 1, p. 67-78

    Research output: Contribution to journalArticlepeer-review

  5. Enumerative geometry of elliptic curves on toric surfaces

    Len, Y. & Ranganathan, D., Jun 2018, In: Israel Journal of Mathematics. 226, p. 351–385

    Research output: Contribution to journalArticlepeer-review

Related by journal

  1. Enumeration of idempotents in diagram semigroups and algebras

    Dolinka, I., East, J., Evangelou, A., FitzGerald, D., Ham, N., Hyde, J. & Loughlin, N., Apr 2015, In: Journal of Combinatorial Theory, Series A. 131, p. 119-152 34 p.

    Research output: Contribution to journalArticlepeer-review

  2. Bounds on the number of small Latin subsquares

    Browning, J., Cameron, P. J. & Wanless, I., May 2014, In: Journal of Combinatorial Theory, Series A. 124, p. 41-56

    Research output: Contribution to journalArticlepeer-review

  3. Combinatorial representations

    Cameron, P. J., Gadouleau, M. & Riis, S., 2013, In: Journal of Combinatorial Theory, Series A. 120, 3, p. 671-682

    Research output: Contribution to journalArticlepeer-review

  4. Substitution-closed pattern classes

    Atkinson, M. D., Ruskuc, N. & Smith, R., Feb 2011, In: Journal of Combinatorial Theory, Series A. 118, 2, p. 317-340

    Research output: Contribution to journalArticlepeer-review

ID: 268424802

Top