Tootfinder

This https://arxiv.org/abs/2412.03532 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A complete theory of smoothable compactified Jacobians of nodal curves
We introduce and study a new class of compactified Jacobians for nodal curves, that we call compactified Jacobians of vine type, or simply V-compactified Jacobians. This class is strictly larger than the class of classical compactified Jacobians, as constructed by Oda-Seshadri, Simpson, Caporaso and Esteves. We characterize V-compactified Jacobians as the compactified Jacobians that can arise as limits of Jacobians of smooth curves under a one-parameter smoothing of the nodal curve, extending…

Don't send me “how are you” questions, let's get to the main point 😌
#corpo #it

This https://arxiv.org/abs/2410.22275 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Piecewise geodesic Jordan curves II: Loewner energy, projective structures, and accessory parameters
In this paper we consider Jordan curves on the Riemann sphere passing through $n \ge 3$ given points. We show that in each relative isotopy class of such curves, there exists a unique curve that minimizes the Loewner energy. These curves have the property that each arc between two consecutive points is a hyperbolic geodesic in the domain bounded by the other arcs. This geodesic property lets us define a complex projective structure whose holonomy lies in $\mathrm{PSL}(2,\mathbb{R})$. We show th…

spotify rant
I really would like to move away from spotify, but bandcamp only sells crappy remix tracks of the stuff that I would like to listen to... Argh.