Giulio Codogni

Research Activity

Ph.D. Thesis: Satake Compactifications, Lattices and Schottky problem, supervised by Prof. N. Shepherd-Barron
Smith-Knight and Rayleigh-Knight Prizes 2013
EPSRC scholarship, and an award from the Department of Pure Mathematics and Mathematical Statistic

Publications:

• The non-existence of stable Schottky forms
  with N. Shepherd-Barron
  Compositio Mathematica, Volume 150, Issue 4. April 2014, pages 679-690

• Fano varieties in Mori Fibre Spaces
  with  A. Fanelli, R. Svaldi and L. Tasin
  Int. Math. Res. Notices, Volume 2016, Issue 7, pages 2026-2067

• Non-reductive automorphism groups, the Loewy filtration and K-stability
  with R. Dervan
  Annales de l’Institut Fourier,  Volume 66,  n. 5, 2016,  pages 1895-1921, Errata Corrige

• Hyperelliptic Schottky Problem and Stable Modular Forms
  Documenta Mathematica 21 , 2016

• The degree of the Gauss map of the theta divisor
  with S. Grushevsky and E. Sernesi
  Algebra and Number Theory, Vol 11, Issue 4, 2017, pages 983-1001 

• Tits buildings and K-stability
  Proceedings of the Edinburgh Mathematical Society, Volume 62, Issue 3, 2019, pages 799-815

• The blow-up of P4 at 8 points and its Fano model, via vector bundles on a degree 1 del Pezzo surface
  with C. Casagrande and A. Fanelli,
  Revista Matemática Complutense, Volume 32, Issue 2, 2019, pages 475-529

• The Gauss map and secants of the Kummar variety
  with R. Auffarth and R. Salvati Manni
  Bulletin of the London Mathematical Society ,  Volume 51, Issue 3, 2019, pages 489-500

• Moduli and Periods of Supersymmetric curves
  with F. Viviani
  Advances in Theoretical and Mathematical Physics, Volume 23 ,Number 2, 2019, pages 345-402

• Theta divisors whose Gauss map has fibers of positive dimension
  with R. Auffarth
  Journal of Algebra,Volume 548, 2020, pages 153-161

• Positivity of the CM line bundle for families of K-stable klt Fanos
  with Zs. Patakfalvi
  Inventiones Mathematicae , Volume 223, Number 3, pages 811-894, 2021

• On some modular contraction of the moduli space of stable pointed curves
  with L. Tasin and F. Viviani
  Algebra and Number Theory,  Vol. 15 (2021), No.4, 1245-1281

• Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: an algebro-geometric approach.
  with E. Arbarello and G. Pareschi
  Crelle's Journal, Volume 2021, Issue 777

• Semincontinuity of the Gauss map and the Schottky problem
  with T. Krämer
  Mathematische Annalen, 382,  607-630 (2022)

• On the first steps of the minimal model program for the moduli space of stable pointed curves
  with L. Tasin and F. Viviani
  Journal of the Institute of Mathematics of Jussieu, Volume 22 , Issue 1 , January 2023 , pp. 145 - 211

• Slope inequalities for KSB-stable and K-stable families
  with L. Tasin and F. Viviani
  Proceedings of the London Mathematical Society, Volume126, Issue4, April 2023, pp. 1394-1465

Other activities

Editorial activities:

• Moduli of K-stable varieties
  with R. Dervan and F. Viviani
  Springer INdAM series, volume 31, 2019 

• De Cifris Seminar
  with D. Bazzanella, N. Murro and R. Zunino
  De Cifris Koine, volume 2, 2024