7 papers
The Martens-Mumford Theorem and the Green-Lazarsfeld Secant Conjecture
Daniele Agostini
The Green-Lazarsfeld secant conjecture predicts that the syzygies of a curve of sufficiently high degree are controlled by its special secants. We prove this conjecture for all cur…
Numerical reconstruction of curves from their Jacobians
Daniele Agostini, Türkü Özlüm Çelik, Demir Eken
We approach the Torelli problem of recostructing a curve from its Jacobian from a computational point of view. Following Dubrovin, we design a machinery to solve this problem effec…
KP Solitons from Tropical Limits
Daniele Agostini, Claudia Fevola, Yelena Mandelshtam +1
We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann's theta function becomes a finite exponential su…
Theta surfaces
Daniele Agostini, Türkü Özlüm Çelik, Julia Struwe +1
A theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This includes surfaces arising from special plane quartics that are singular or reducible.…
Computing Theta Functions with Julia
Daniele Agostini, Lynn Chua
We present a new package Theta.jl for computing with the Riemann theta function. It is implemented in Julia and offers accurate numerical evaluation of theta functions with charact…
On the Schottky problem for genus five Jacobians with a vanishing theta null
Daniele Agostini, Lynn Chua
We give a solution to the weak Schottky problem for genus five Jacobians with a vanishing theta null, answering a question of Grushevsky and Salvati Manni. More precisely, we show…