Skip to content

Research at St Andrews

Lifting tropical bitangents

Research output: Contribution to journalArticlepeer-review

Author(s)

Yoav Len, Hannah Markwig

School/Research organisations

Abstract

We study lifts of tropical bitangents to the tropicalization of a given complex algebraic curve together with their lifting multiplicities. Using this characterization, we show that generically all the seven bitangents of a smooth tropical plane quartic lift in sets of four to algebraic bitangents. We do this constructively, i.e. we give solutions for the initial terms of the coefficients of the bitangent lines. This is a step towards a tropical proof that a general smooth quartic admits 28 bitangent lines. The methods are also appropriate to count real bitangents, however the conditions to determine whether a tropical bitangent has real lifts are not purely combinatorial.
Close

Details

Original languageEnglish
Pages (from-to)122-152
JournalJournal of Symbolic Computation
Volume96
Early online date1 Mar 2019
DOIs
Publication statusPublished - Jan 2020

    Research areas

  • Tropical geometry, Bitangents of quartics

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 self intersections

    Len, Y. & Satriano, M., Feb 2020, In: Journal of Combinatorial Theory, Series A. 170, 21 p., 105138.

    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. Polynomial-time proofs that groups are hyperbolic

    Holt, D., Linton, S., Neunhoeffer, M., Parker, R., Pfeiffer, M. & Roney-Dougal, C. M., May 2021, In: Journal of Symbolic Computation. 104, p. 419-475

    Research output: Contribution to journalArticlepeer-review

  2. Computing finite semigroups

    East, J., Egri-Nagy, A., Mitchell, J. D. & Péresse, Y., May 2019, In: Journal of Symbolic Computation. 92, p. 110-155 46 p.

    Research output: Contribution to journalArticlepeer-review

  3. New refiners for permutation group search

    Jefferson, C., Pfeiffer, M. & Waldecker, R., May 2019, In: Journal of Symbolic Computation. 92, p. 70-92 23 p.

    Research output: Contribution to journalArticlepeer-review

  4. Integrality and arithmeticity of solvable linear groups

    Detinko, A., Flannery, D. & de Graaf, W., 2015, In: Journal of Symbolic Computation. 68, p. 138–145

    Research output: Contribution to journalArticlepeer-review

ID: 268424731

Top