Pietro Beri

About me 

I am currently a postdoc in Institut de Mathématiques de Jussieu-Paris Rive Gauche (IMJ-PRG), Université de Paris, funded by the ERC Synergy Grant HyperK, mentored by  Olivier Debarre .

Previously I was ATER (teaching and research assistant) at the Institut de mathématiques de Toulouse, Université Paul Sabatier.

I obtained my PhD in Mathematics at Université de Poitiers in october 2020 under the supervision of Alessandra Sarti.  Click here  for a detailed CV. For a french version click here  .

Research interest

My research field is complex algebraic geometry. More precisely, I work on Hyper-Kähler manifolds, in particular: 

• Moduli spaces, their Kodaira dimension, their divisors, moduli spaces of Hyper-Kähler manifolds with an involution, rational maps between them;  

• linear systems, base locus and image;

• biregular and birational automorphism, classification and geometric description;

• birational geometry, birational model of Hyper-Kähler manifolds, MMP;

• locally complete families of Hyper-Kähler manifolds;

• double EPW sextics and their link with Gushel-Mukai varieties;

• cohomology of Hyper-Kähler manifolds.

Preprints and publications

1. With Alberto Cattaneo, "On birational transformations of Hilbert schemes of points on K3 surfaces" Mathematische Zeitschrift 301.2 (2022): 1537-1554, arxiv.org/abs/2005.05187 .

2. "EPW sextics associated to K3 surfaces", https://arxiv.org/abs/2011.12223 .

3. With Olivier Debarre, "On the Hodge and Betti numbers of hyper-Kähler manifolds", Milan Journal of Mathematics (2022): 1-15, Betti.pdf .

4. With Laurent Manivel, "A birational involution", submitted, https://arxiv.org/abs/2211.12866 

5.  With Ignacio Barros, Emma Brakkee, Laure Flapan, "Kodaira dimension of moduli spaces of hyperkähler varieties", submitted, arxiv.org/abs/2212.12586 .