Research
My research is mainly focused on irreducible holomorphic symplectic (ihs) varieties, smooth and singular, especially when arising as moduli spaces of semistable sheaves on K3 and abelian surfaces. I am particulary interested in geometrical problems on such varieties, as for instance:
the existence of ample uniruled divisors on ihs, with releted consequences on their Chow groups
the singularity type of singular moduli spaces, via Hodge theory
rational maps between ihs of different deformation type
construction of singular examples as quotient of smooth ihs via a symplectic action.
Preprints
Terminalizations of quotients of compact hyperkähler manifolds by induced symplectic automorphisms, V. Bertini, A. Grossi, M. Mauri and E. Mazzon, preprint arXiv:2401.13632.
Publications
Rational curves on primitive symplectic varieties of OG6 singular type, V. Bertini and A. Grossi. Math. Z. 304, 36 (2023). View online version available here.
Hodge structure of singular O'Grady's moduli spaces, V. Bertini and F. Giovenzana. To appear in Annali della SNS di Pisa, preprint arXiv:2203.07917.
Rational curves on O'Grady's tenfolds, V. Bertini. To appear in Kyoto Journal of Mathematics, preprint arXiv:2101.01029.
PhD Thesis
Rational curves on irreducible holomorphic symplectic varieties of OG10-type. Please note that this version contains errors in the statement of Proposition 5.2.3 and Proposition 6.1.17,(2), and consequently in the statement of Theorem 5.3.1, Theorem 6.1.5 and Corollary 6.1.9, based on the intersection computed in the previous propositions. You can find here the correct statements and proofs.