Results 1 to 10 of about 36 (34)

Tropicalization of the universal Jacobian [PDF]

Épijournal de Géométrie Algébrique, 2022
In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli ...
Margarida Melo, Samouil Molcho, Martin Ulirsch, Filippo Viviani   +3 more
doaj   +1 more source

Brill-Noether theory for curves of a fixed gonality

Forum of Mathematics, Pi, 2021
We prove a generalisation of the Brill-Noether theorem for the variety of special divisors $W^r_d(C)$ on a general curve C of prescribed gonality. Our main theorem gives a closed formula for the dimension of $W^r_d(C)$ . We build on previous
David Jensen, Dhruv Ranganathan
doaj   +1 more source

A MODULI STACK OF TROPICAL CURVES

Forum of Mathematics, Sigma, 2020
We contribute to the foundations of tropical geometry with a view toward formulating tropical moduli problems, and with the moduli space of curves as our main example.
RENZO CAVALIERI, MELODY CHAN, MARTIN ULIRSCH, JONATHAN WISE   +3 more
doaj   +1 more source

Haas' theorem revisited [PDF]

Épijournal de Géométrie Algébrique, 2017
Haas' theorem describes all partchworkings of a given non-singular plane tropical curve $C$ giving rise to a maximal real algebraic curve. The space of such patchworkings is naturally a linear subspace $W_C$ of the $\mathbb{Z}/2\mathbb{Z}$-vector space $\
Benoît Bertrand, Erwan Brugallé, Arthur Renaudineau   +2 more
doaj   +1 more source

Orthogonality for (0, −1) tropical normal matrices

Special Matrices, 2020
We study pairs of mutually orthogonal normal matrices with respect to tropical multiplication. Minimal orthogonal pairs are characterized. The diameter and girth of three graphs arising from the orthogonality equivalence relation are computed.
Bakhadly Bakhad, Guterman Alexander, de la Puente María Jesús   +2 more
doaj   +1 more source

Lefschetz (1,1)-theorem in tropical geometry [PDF]

Épijournal de Géométrie Algébrique, 2018
For a tropical manifold of dimension n we show that the tropical homology classes of degree (n-1, n-1) which arise as fundamental classes of tropical cycles are precisely those in the kernel of the eigenwave map.
Philipp Jell, Johannes Rau, Kristin Shaw
doaj   +1 more source

CANONICAL REPRESENTATIVES FOR DIVISOR CLASSES ON TROPICAL CURVES AND THE MATRIX–TREE THEOREM

Forum of Mathematics, Sigma, 2014
Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit ...
YANG AN, MATTHEW BAKER, GREG KUPERBERG, FARBOD SHOKRIEH   +3 more
doaj   +1 more source

A metric graph satisfying w41=1$w_4^1 = 1$ that cannot be lifted to a curve satisfying dim⁡ (W41)=1$\dim \;(W_4^1 ) = 1$

Open Mathematics, 2016
For all integers g ≥ 6 we prove the existence of a metric graph G with w41=1$w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric ...
Coppens Marc
doaj   +1 more source

HYPERELLIPTIC GRAPHS AND METRIZED COMPLEXES

Forum of Mathematics, Sigma, 2017
We prove a version of Clifford’s theorem for metrized complexes. Namely, a metrized complex that carries a divisor of degree $2r$ and rank
YOAV LEN
doaj   +1 more source

MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY

Forum of Mathematics, Sigma, 2016
We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector $w$ of weights, the moduli ...
RENZO CAVALIERI, SIMON HAMPE, HANNAH MARKWIG, DHRUV RANGANATHAN   +3 more
doaj   +1 more source