K3 surfaces with a symplectic action of $(\mathbb Z/2\mathbb Z)^2$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910550822223872 |
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| author | Piroddi, Benedetta |
| author_facet | Piroddi, Benedetta |
| contents | We study the symplectic action of the group (Z/2Z)^2 on a K3 surface X: we describe its action on H^2(X,Z) and the maps induced in cohomology by the rational quotient maps; we give a lattice-theoretic characterization of the resolution of singularities of the quotient X/i, where i is any of the involutions in (Z/2Z)^2. Assuming X is projective, we describe the correspondence between irreducible components of its moduli space, and those of the resolution of singularities of its quotients: this being the first description of this correspondence for a non-cyclic action, we see new phenomena, of which we provide explicit examples assuming $X$ has a polarization of degree 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K3 surfaces with a symplectic action of $(\mathbb Z/2\mathbb Z)^2$ Piroddi, Benedetta Algebraic Geometry 14J28, 14J50, 14J27 We study the symplectic action of the group (Z/2Z)^2 on a K3 surface X: we describe its action on H^2(X,Z) and the maps induced in cohomology by the rational quotient maps; we give a lattice-theoretic characterization of the resolution of singularities of the quotient X/i, where i is any of the involutions in (Z/2Z)^2. Assuming X is projective, we describe the correspondence between irreducible components of its moduli space, and those of the resolution of singularities of its quotients: this being the first description of this correspondence for a non-cyclic action, we see new phenomena, of which we provide explicit examples assuming $X$ has a polarization of degree 4. |
| title | K3 surfaces with a symplectic action of $(\mathbb Z/2\mathbb Z)^2$ |
| topic | Algebraic Geometry 14J28, 14J50, 14J27 |
| url | https://arxiv.org/abs/2408.00643 |