5 papers
PCMI lecture notes: Motivic explorations in enumerative geometry
Sabrina Pauli
These are lecture notes for the PCMI 2024 Graduate Summer School for the mini-workshop on motivic explorations in enumerative geometry. Motivic homotopy theory allows to do enumera…
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…
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…
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…