9 papers · 1 filter
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…
Cohomology classes on moduli of curves from Theta Characteristics
Andrés Jaramillo Puentes, Roberto Pirisi
Using Galois-Stiefel-Whitney classes of theta characteristics we show that over a totally real base field the moduli stack of smooth genus curves and the moduli stack of princi…
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…
A Wall Crossing Formula for Motivic Enumerative Invariants
Andrés Jaramillo Puentes
We prove an analog of the wall crossing formula for Welschinger invariants relating the difference of signed curve counting of real curves passing through configurations that diffe…
Arithmetic Counts of Tropical Plane Curves and Their Properties
Andrés Jaramillo Puentes, Hannah Markwig, Sabrina Pauli +1
Recently, the first and third author proved a correspondence theorem which recovers the Levine-Welschinger invariants of toric del Pezzo surfaces as a count of tropical curves weig…
A Quadratically Enriched Correspondence Theorem
Andrés Jaramillo Puentes, Sabrina Pauli
We quadratically enrich Mikhalkin's correspondence theorem. That is, we prove a correspondence between algebraic curves on a toric surface counted with Levine's quadratic enrichmen…
Trigonal Morsifications on Hirzebruch Surfaces with an appendix by E. Shustin
Andrés Jaramillo Puentes
In this paper we obtain a classification of rigid isotopy classes of totally reducible trigonal curves lying on a Hirzebruch surface , and having a maximal number of non-degen…
Rigid isotopy classification of generic rational quintics in
Andrés Jaramillo Puentes
In this article we obtain the rigid isotopy classification of generic rational curves of degre in . In order to study the rigid isotopy classes of nod…
Generic pointed quartic curves in and uninodal dessins
Andrés Jaramillo Puentes
In this article we obtain a rigid isotopy classification of generic pointed quartic curves in by studying the combinatorial properties of dessins…