Publications by Giulio Codogni

Supersingular Curves You Can Trust

Tako Boris Fouotsa, Benjamin Pierre Charles Wesolowski, Giulio Codogni

Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a notoriously hard task, despite several isogeny-based protocols relying on such an object. A trusted setup is often proposed as a workaround, but several aspects rem ...

2023

Positivity of the CM line bundle for families of K-stable klt Fano varieties

Zsolt Patakfalvi, Giulio Codogni

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...

2021

Tits Buildings And K-Stability

Giulio Codogni

A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits ...

CAMBRIDGE UNIV PRESS2019

NON-REDUCTIVE AUTOMORPHISM GROUPS, THE LOEWY FILTRATION AND K-STABILITY (vol 66, pg 1895, 2016)

Giulio Codogni

ANNALES INST FOURIER2018

A note on the fibres of Mori fibre spaces

Giulio Codogni, Roberto Svaldi

We consider the problem of determining which Fano manifolds can be realised as fibres of a Mori fibre space. In particular, we study the case of toric varieties, Fano manifolds with high index and some Fano manifolds with high Picard rank. ...

SPRINGER INTERNATIONAL PUBLISHING AG2018