8 papers
Quadratically Enriched Plane Curve Counting via Tropical Geometry
Andrés Jaramillo Puentes, Hannah Markwig, Sabrina Pauli +1
We prove that the quadratically enriched count of rational curves in a smooth toric del Pezzo surface passing through -rational points and pairs of conjugate points in quadratic…
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…
A lifting partition theorem for tropical tritangent classes to smooth space sextic curves
Maria Angelica Cueto, Hannah Markwig, Yue Ren
The set of tritangent planes to smooth tropical space sextic curves has 15 connected components, recording continuous displacements of planes preserving the tritangency condition.…
Trigonal and embedded tropical curves of low genus
Hannah Markwig, Angelina Zheng
In algebraic geometry, trigonal curves can always be embedded into Hirzebruch surfaces. In tropical geometry, the notion of trigonality does not have a unique translation. We focus…
Tropical Methods for Counting Plane Curves -- Complex, Real and Quadratically Enriched
Andrés Jaramillo Puentes, Hannah Markwig, Sabrina Pauli +1
Since the first famous correspondence theorem by Mikhalkin appeared in 2005, tropical geometry has allowed a parallel treatment of real and complex counting problems. A prime examp…
One part leaky covers
Renzo Cavalieri, Hannah Markwig, Johannes Schmitt
In our previous work [CMS24] we defined a new class of enumerative invariants called -leaky double Hurwitz descendants, generalizing both descendant integrals of double ramifica…