November 18, 2025Rendiconti del Circolo Matematico di Palermo Series 2Open Access

Geometric realizations of non-symplectic involutions on the Hilbert square of a K3 surface

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New involutions are identified in the Hilbert scheme of K3 surfaces, enhancing understanding of these geometries.
The study offers insights into their automorphism group, particularly in relation to known results and examples.
Analysis of geometric constructions provides a framework for exploring non-symplectic properties of IHS manifolds.
These findings extend current knowledge of K3 surfaces, potentially guiding future research directions.

Implication

New examples of involutions in IHS manifolds reveal insights on the automorphism group of Hilbert schemes.

Abstract

We give new examples of geometric constructions of non-natural non-symplectic involutions of IHS manifolds whose existence is guaranteed by previous results of Bossiére-Cattaneo-Nieper-Wiesskirchen-Sarti as reported by Boissiére (The automorphism group of the Hilbert scheme of two points on a generic projective K3 surface, Springer, Cham, 2016) and Bossière-Camere-Sarti in (Kyoto J Math 56: 465–499, 2016).

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Cite This Study

Ana Quedo (2025) studied this question.

synapsesocial.com/papers/6924fef4c0ce034ddc351c82 https://doi.org/10.1007/s12215-025-01342-1

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Implication

New examples of involutions in IHS manifolds reveal insights on the automorphism group of Hilbert schemes.

Geometric realizations of non-symplectic involutions on the Hilbert square of a K3 surface

Key Points

Implication

Abstract

Discussion

Cite This Study

Geometric realizations of non-symplectic involutions on the Hilbert square of a K3 surface

Key Points

Implication

Abstract

Discussion

Cite This Study

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