2 citations · 3 across the 6 of their papers we have counts for
7 papers · 1 filter
On Frobenius' theta formula
Alessio Fiorentino, Riccardo Salvati Manni
Mumford's well-known characterization of the hyperelliptic locus of the moduli space of ppavs in terms of vanishing and non-vanishing theta constants is based on Neumann's dynamica…
Weber's formula for the bitangents of a smooth plane quartic
Alessio Fiorentino
In a section of his 1876 treatise Theorie der Abel'schen Functionen vom Geschlecht 3 Weber proved a formula that expresses the bitangents of a non-singular plane quartic in terms o…
A new proof of the Caporaso-Sernesi theorem via Weber's formula
Francesco Dalla Piazza, Alessio Fiorentino
In this paper we give a new proof of Caporaso and Sernesi's result which states that the general plane quartic is uniquely determined by its 28 bitangents. Our proof uses classical…
Vector-valued modular forms and the Gauss map
Francesco Dalla Piazza, Alessio Fiorentino, Samuel Grushevsky +2
We use the gradients of theta functions at odd two-torsion points --- thought of as vector-valued modular forms --- to construct holomorphic differential forms on the moduli space…
Plane quartics: the matrix of bitangents
Francesco Dalla Piazza, Alessio Fiorentino, Riccardo Salvati Manni
Aronhold's classical result states that a plane quartic can be recovered by the configuration of any Aronhold systems of bitangents, i.e. special 7-tuples of bitangents such that t…
A new geometric description for Igusa's modular form
Alessio Fiorentino
The modular form notably appears in one of Igusa's classic structure theorems as a generator of the ring of full modular forms in genus 2, being exhibited by means of a c…
On a ring of modular forms related to the Theta gradients map in genus 2
Alessio Fiorentino
The level moduli space is mapped to the projective space by means of gradients of odd Theta functions, such a map turning out no to be injective in the genus 2 case. In…