8 papers · 1 filter
Ulrich sheaves, the arithmetic writhe and algebraic isotopies of space curves
Daniele Agostini, Mario Kummer
We establish a connection between the theory of Ulrich sheaves and -homotopy theory. For instance, we prove that the -degree of a morphism between proje…
On the irrationality of moduli spaces of projective hyperkähler manifolds
Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
The aim of this paper is to estimate the irrationality of moduli spaces of hyperkähler manifolds of types K3, Kum, OG6, and OG10. We prove that the degrees of irratio…
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.…