26 citations · 130 across the 20 of their papers we have counts for
22 papers
Hodge integrals on admissible covers and tautological projections of Prym classes
Yoav Len, Sam Molcho, Navid Nabijou
In the moduli space of abelian varieties, Prym loci parametrise Prym varieties associated to covers of curves with fixed degree and monodromy data. We derive and implement an algor…
Tropical methods for building real space sextics with totally real tritangent planes
Maria Angelica Cueto, Yoav Len, Hannah Markwig +1
This paper proposes the use of combinatorial techniques from tropical geometry to build the 120 tritangent planes to a given smooth algebraic space sextic. Although the tropical co…
On gonality-tight graphs
Šimun Dropuljić, Yoav Len
We address a question posed by Fessler--Jensen--Kelsey--Owen regarding graphs whose second gonality is greater than the first by exactly 1. We answer the question affirmatively und…
The tropical Abel--Prym map
Giusi Capobianco, Yoav Len
We prove that the tropical Abel--Prym map associated with a free double cover of hyperelliptic metric graphs…
Chip-firing games, Jacobians, and Prym varieties
Yoav Len
We present a self-contained introduction to the theory of chip-firing games on metric graphs, as well as the more recent theory of tropical Prym varieties. We briefly discuss the c…
Tropical tangents for complete intersection curves
Nathan Ilten, Yoav Len
We consider the tropicalization of tangent lines to a complete intersection curve in . Under mild hypotheses, we describe a procedure for computing the tropicaliz…
Kirchhoff's theorem for Prym varieties
Yoav Len, Dmitry Zakharov
We prove an analogue of Kirchhoff's matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms…
Prym-Brill-Noether Loci of special curves
Steven Creech, Yoav Len, Caelan Ritter +1
We use Young tableaux to compute the dimension of , the Prym-Brill-Noether locus of a folded chain of loops of any gonality. This tropical result yields a new upper bound on t…
Abelian tropical covers
Yoav Len, Martin Ulirsch, Dmitry Zakharov
Let be a finite abelian group. In this article, we classify harmonic -covers of a tropical curve (which allow dilation along edges and at vertices)…
Skeletons of Prym varieties and Brill--Noether theory
Yoav Len, Martin Ulirsch
We show that the non-Archimedean skeleton of the Prym variety associated to an unramified double cover of an algebraic curve is naturally isomorphic (as a principally polarized tro…
Lifting tropical self intersections
Yoav Len, Matthew Satriano
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…
Projective duals to algebraic and tropical hypersurfaces
Nathan Ilten, Yoav Len
We study a tropical analogue of the projective dual variety of a hypersurface. When is a curve in or a surface in , we provide an explicit descript…
Bitangents of non-smooth tropical quartics
Heejong Lee, Yoav Len
We study bitangents of non-smooth tropical plane quartics. Our main result is that with appropriate multiplicities, every such curve has 7 equivalence classes of bitangent lines. M…
Lifting tropical bitangents
Yoav Len, Hannah Markwig
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 tha…
Tritangent planes to space sextics: the algebraic and tropical stories
Corey Harris, Yoav Len
We discuss the classical problem of counting planes tangent to general canonical sextic curves at three points. We determine the number of real tritangents when such a curve is rea…
Tropicalization of theta characteristics, double covers, and Prym varieties
David Jensen, Yoav Len
We study the behavior of theta characteristics on an algebraic curve under the specialization map to a tropical curve. We show that each effective theta characteristic on the tropi…
Hyperelliptic graphs and metrized complexes
Yoav Len
We prove a version of Clifford's theorem for metrized complexes. Namely, a metrized complex that carries a divisor of degree and rank (for ) also carries a diviso…
Enumerative geometry of elliptic curves on toric surfaces
Yoav Len, Dhruv Ranganathan
We establish the equality of classical and tropical curve counts for elliptic curves on toric surfaces with fixed -invariant, refining results of Mikhalkin and Nishinou--Siebert…
A note on algebraic rank, matroids, and metrized complexes
Yoav Len
We show that the algebraic rank of divisors on certain graphs is related to the realizability problem of matroids. As a consequence, we produce a series of examples in which the al…
Bitangents of tropical plane quartic curves
Matt Baker, Yoav Len, Ralph Morrison +2
We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For…
Algebraic and combinatorial rank of divisors on finite graphs
Lucia Caporaso, Yoav Len, Margarida Melo
We study the algebraic rank of a divisor on a graph, an invariant defined using divisors on algebraic curves dual to the graph. We prove it satisfies the Riemann-Roch formula, a sp…
The Brill-Noether rank of a tropical curve
Yoav Len
We construct a space classifying divisor classes of a fixed degree on all tropical curves of a fixed combinatorial type and show that the function taking a divisor class to its ran…