Marseille Mathematics Institute

Aix-Marseille University
Campus Saint Charles
Marseille
France

Email: manivel@math.cnrs.fr

Research interests
Complex algebraic geometry
Homogeneous spaces and representations of algebraic groups
Quantum cohomology and derived categories
Geometric Complexity

Editor of the Journal de Mathématiques Pures et Appliquées, also known as Liouville's journal. Send your best papers!

FanoBase

A collaborative project (with Pieter Belmans, Vladimiro Benedetti, Francesco Denisi, Enrico Fatighenti, Javier Fernandez Piriz, Alessandro Frassineti, Federico Papa, Fabio Tanturri, and Federico Tufo), devoted to the study and classification of smooth Fano fourfolds.

Type-A website (beta release), Blog.

News

Algebraic Geometry 2026, a birthday conference in Vason, Italy. Thanks to the organizers!

The FanoHK project (From Fano manifolds to HyperKähler varieties), funded by the ANR, started in April 2021 and ended on October 2026.
The main conference of the project took place in Toulouse, December 15 to 19, 2025.

Preprints

• An atomic criterion for irrationality without quantum computations
  with V. Benedetti, A. Fay, J. Guéré, N. Perrin, 7 pages, arXiv:2607.26718.
  
  
• Quantum cohomology and birational geometry of Verra fourfolds
  with V. Benedetti, J. Guéré, N. Perrin, 13 pages, arXiv:2605.30450.
  
  
• Spinorial Fano manifolds
  with A. Frassineti, 19 pages, arXiv:2605.28712.
  
  
• Quantum cohomology and irrationality of Gushel-Mukai fourfolds
  with V. Benedetti, N. Perrin, 16 pages, arXiv:2603.17487.
  
  
• More birational involutions
  with P. Beri, 49 pages, arXiv:2509.10130.
  
  
• BRIDGES Lectures: G2 in action, and a mathematical theory of exceptions
  70 pages, arXiv:2508.12757.
  
  
• Göpel varieties
  with V. Benedetti, M. Bolognesi, D. Faenzi, 48 pages, arXiv:2506.22030.
  
  
• On linear sections of the spinor tenfold II
  with Y. Liu, 48 pages, arXiv:2504.21056.
  
  
• Even nodal surfaces of K3 type
  with M. Bernardara, E. Fatighenti, G. Kapustka, M. Kapustka, G. Mongardi and F. Tanturri
  30 pages, arXiv:2402.08528.
  
  
• A birational involution
  with P. Beri, 43 pages, arXiv:2211.12866.
  
  
• Fano fourfolds of K3 type
  with M. Bernardara, E. Fatighenti and F. Tanturri, 66 pages, arXiv:2111.13030, to appear in AIF.
  
  

Recent publications

• F4 and desmic surfaces
  Annals of Global Geometry and Analysis 69 (3), 2026.
  
  
• Hecke cycles on moduli of vector bundles and orbital degeneracy loci
  with V. Benedetti, M. Bolognesi, D. Faenzi, JAG 35 (2026), 163-195.
  
  
• Proof of a conjecture of Sturmfels, Timme and Zwiernik
  in Varieties, Polyhedra, Computation, EMS Series of Congress Reports, 2025.
  
  
• Equivariant spaces of matrices of constant rank
  with J.M. Landsberg, Pure and Applied Mathematics Quarterly 21 (2025), 1209-1244.
  
  
• Discriminants of theta-representations
  with V. Benedetti, Ann. Sc. Norm. Super. Pisa 25 (2024), 2125-2148t.
  
  
• On the automorphisms of hyperplane sections of generalized Grassmannians
  with V. Benedetti, Transformation Groups 29 (2024), 1115-1159.
  
  
• Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming
  with M. Michalek, L. Monin, T. Seynnaeve, M. Vodicka, JEMS 26 (2024), 3091–3135.
  
  
• The Coble quadric
  with V. Benedetti, M. Bolognesi, D. Faenzi, Forum Math. Sigma 12 (2024), Paper e63, 25 pages.
  
  
• A four dimensional cousin of the Segre cubic
  Rev. Mat. Iberoamericana 40 (2024), 1089-1114.
  
  
• Matrices of linear forms of constant rank from vector bundles on projective spaces
  with R.M. Miro-Roig, Adv. Math. 436 (2024), Paper No. 109408, 42 pages.