Giacomo Nanni

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math.AG2025

Lagrangian fibrations on Nikulin-type orbifolds

Giacomo Nanni

We classify lagrangian fibrations on Nikulin orbifolds, a well studied class of singular irreducible holomorphic symplectic varieties, and prove they verify the SYZ conjecture.

math.AG2025

Monodromy of Nikulin orbifolds

Giacomo Nanni

We give a new proof for the maximality of the monodromy group of a Nikulin orbifold, a symplectic orbifold arising as terminalisation of a symplectic quotient of a $K 3^{[2]}$ -type…

math.AG2023

Classification of Lagrangian planes in generalised Kummer manifolds

Giacomo Nanni

We prove that the class of a line contained in a Lagrangian plane on a dimension $2 n$ hyperkähler manifold $X$ of Kummer type has Beauville-Bogomolov-Fujiki square $- \frac{n + 1}{2}$ …