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October 5, 2025Open Access

The SYZ conjecture for singular moduli spaces of sheaves on K3 surfaces

Key Points

The study proves the SYZ conjecture for irreducible symplectic varieties, which are deformation equivalent to moduli spaces of sheaves.
The key evidence includes generalizing previous results about lagrangian fibrations in the singular settings of symplectic varieties.
An assessment of the Huybrechts–Riemann–Roch polynomial and its polarisation type provides additional insight into these symplectic varieties.
The implications highlight the significance of these findings for understanding complex geometrical structures and their applications.

Abstract

In this paper we prove the SYZ conjecture for irreducible symplectic varieties that are locally trivial deformation equivalent to moduli spaces of sheaves on K3 surfaces. As an intermediate step in the argument, we generalise to the singular setting a result of Kamenova--Verbitsky and Matsushita about moduli spaces of lagrangian fibrations of primitive symplectic varieties. Two further corollaries are also presented: the computation of the Huybrechts--Riemann--Roch polynomial and of the polarisation type of this kind of symplectic varieties.

The SYZ conjecture for singular moduli spaces of sheaves on K3 surfaces

Key Points

Abstract

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