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math.AG2025

Numerical invariants of hyper-Kähler manifolds

Olivier Debarre, Chen Jiang

We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-Kähler manifolds, mostly in dimension 6 and in the presence of an…

math.AG2025

An effective upper bound for Fano indices of canonical Fano threefolds, I

Chen Jiang, Haidong Liu

Let be a -factorial weak Fano -fold with at worst isolated canonical singularities. We show that the -Fano index of is at most .

math.AG2025

Total Cartier index of a bounded family

Jingjun Han, Chen Jiang

We prove that the total Cartier index of a bounded family of projective varieties of klt type is bounded.