16 citations · 64 across the 18 of their papers we have counts for
22 papers
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…
Vector Spaces of Generalized Euler Integrals
Daniele Agostini, Claudia Fevola, Anna-Laura Sattelberger +1
We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman in…
Recovery of Plane Curves from Branch Points
Daniele Agostini, Hannah Markwig, Clemens Nollau +3
We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch points respectively. The plane Hurw…
On Algebraic Theta Divisors and Rational Solutions of the KP Equation
Daniele Agostini, Türkü Özlüm Çelik, John B. Little
In this paper we classify the singular curves whose theta divisors in their generalized Jacobians are algebraic, meaning that they are cut out by polynomial analogs of theta functi…
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…
Likelihood Degenerations
Daniele Agostini, Taylor Brysiewicz, Claudia Fevola +3
Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points…
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…
On the irrationality of moduli spaces of K3 surfaces
Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
We study how the degrees of irrationality of moduli spaces of polarized K3 surfaces grow with respect to the genus . We prove that the growth is bounded by a polynomial function…
Pencils on surfaces with normal crossings and the Kodaira dimension of
Daniele Agostini, Ignacio Barros
We study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we show that the canonical divisor of is not pseudo-effec…
The Dubrovin threefold of an algebraic curve
Daniele Agostini, Türkü Özlüm Çelik, Bernd Sturmfels
The solutions to the Kadomtsev-Petviashvili equation that arise from a fixed complex algebraic curve are parametrized by a threefold in a weighted projective space, which we name a…
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.…
On the Prym map for cyclic covers of genus two curves
Daniele Agostini
The Prym map assigns to each covering of curves a polarized abelian variety. In the case of unramified cyclic covers of curves of genus two, we show that the Prym map is ramified p…
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…
Moment Identifiability of Homoscedastic Gaussian Mixtures
Daniele Agostini, Carlos Améndola, Kristian Ranestad
We consider the problem of identifying a mixture of Gaussian distributions with same unknown covariance matrix by their sequence of moments up to certain order. Our approach rests…
Discrete Gaussian distributions via theta functions
Daniele Agostini, Carlos Améndola
We study a discrete analogue of the classical multivariate Gaussian distribution. It is supported on the integer lattice and is parametrized by the Riemann theta function. Over the…
Asymptotic syzygies and higher order embeddings
Daniele Agostini
We show that vanishing of asymptotic p-th syzygies implies p-very ampleness for line bundles on arbitrary projective schemes. For smooth surfaces we prove that the converse holds w…
Higher syzygies on surfaces with numerically trivial canonical bundle
Daniele Agostini, Alex Küronya, Victor Lozovanu
We characterize property on a polarized surface with trivial canonical bundle in terms of the (non)existence of certain forbidden subvarieties of .
A note on homogeneous ideals of polarized abelian surfaces
Daniele Agostini
Gross and Popescu conjectured that the homogeneous ideal of an embedded -polarized abelian surface is generated by quadrics and cubics for . We prove this using the…
The maximum likelihood degree of Fermat hypersurfaces
Daniele Agostini, Davide Alberelli, Francesco Grande +1
We study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in statistical optimization: maximum likel…