On the transcendental lattices of Hyperk\"ahler manifolds
We introduce the notion of a Hyper-K\"{a}hler manifold $X$ induced by a Hodge structure of K3-type. We explore this notion for the known deformation types of hyper-K\"{a}hler manifolds studying those that are induced by a K3 or abelian surface, giving lattice-theoretic criteria to decide w...
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| creator | Piroddi, Benedetta Ortiz, Ángel David Ríos |
| description | We introduce the notion of a Hyper-K\"{a}hler manifold $X$ induced by a Hodge
structure of K3-type. We explore this notion for the known deformation types of
hyper-K\"{a}hler manifolds studying those that are induced by a K3 or abelian
surface, giving lattice-theoretic criteria to decide whether or not they are
birational to a moduli space of sheaves over said surface. We highlight the
different behaviors we find for the particular class of hyper-K\"{a}hler
manifolds of O'Grady type. |
| doi_str_mv | 10.48550/arxiv.2308.12869 |
| format | Article |
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structure of K3-type. We explore this notion for the known deformation types of
hyper-K\"{a}hler manifolds studying those that are induced by a K3 or abelian
surface, giving lattice-theoretic criteria to decide whether or not they are
birational to a moduli space of sheaves over said surface. We highlight the
different behaviors we find for the particular class of hyper-K\"{a}hler
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hyper-K\"{a}hler manifolds studying those that are induced by a K3 or abelian
surface, giving lattice-theoretic criteria to decide whether or not they are
birational to a moduli space of sheaves over said surface. We highlight the
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structure of K3-type. We explore this notion for the known deformation types of
hyper-K\"{a}hler manifolds studying those that are induced by a K3 or abelian
surface, giving lattice-theoretic criteria to decide whether or not they are
birational to a moduli space of sheaves over said surface. We highlight the
different behaviors we find for the particular class of hyper-K\"{a}hler
manifolds of O'Grady type.</abstract><doi>10.48550/arxiv.2308.12869</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry |
| title | On the transcendental lattices of Hyperk\"ahler manifolds |
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