Riccardo Carini

activity

20222026

collaborators

4 papers

math.AG2026

Irreducible symplectic varieties via K3-del Pezzo double covers

Riccardo Carini

We construct a series of irreducible symplectic varieties of dimension $2 n$ , for $2 \leq n \leq 10$ , with second Betti numbers $16 \leq b_{2} \leq 24$ . They arise as non-trivial terminal…

math.AG2026

Semi-rigid stable sheaves: a criterion and examples

Alessio Bottini, Riccardo Carini

Inspired by Mukai's work on K3 surfaces, we introduce and study a notion of semi-rigidity for stable sheaves on smooth polarised varieties, designed to capture the existence of sta…

math.AG2024

Holomorphic symplectic manifolds from semistable Higgs bundles

Roland Abuaf, Riccardo Carini

Let $M_{C} (2, 0)$ be the moduli space of semistable rank two and degree zero Higgs bundles on a smooth complex hyperelliptic curve $C$ of genus three. We prove that the q…

math.AG2022

One-dimensional Local Families of Complex K3 Surfaces

Riccardo Carini, Francesco Viganò

For any complex K3 surface $X$ , we construct a one-dimensional deformation in which all integers $ρ$ with $0 \leq ρ \leq 20$ occur as Picard numbers of some fibres. In contrast, we…