Non-trivial smooth families of $K3$ surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929232992534528 |
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| author | Baraglia, David |
| author_facet | Baraglia, David |
| contents | Let $X$ be a complex $K3$ surface, ${\rm Diff}(X)$ the group of diffeomorphisms of $X$ and ${\rm Diff}_0(X)$ the identity component. We prove that the fundamental group of ${\rm Diff}_0(X)$ contains a free abelian group of countably infinite rank as a direct summand. The summand is detected using families Seiberg--Witten invariants. The moduli space of Einstein metrics on $X$ is used as a key ingredient in the proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_06354 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-trivial smooth families of $K3$ surfaces Baraglia, David Differential Geometry Geometric Topology 57K41, 57R50 Let $X$ be a complex $K3$ surface, ${\rm Diff}(X)$ the group of diffeomorphisms of $X$ and ${\rm Diff}_0(X)$ the identity component. We prove that the fundamental group of ${\rm Diff}_0(X)$ contains a free abelian group of countably infinite rank as a direct summand. The summand is detected using families Seiberg--Witten invariants. The moduli space of Einstein metrics on $X$ is used as a key ingredient in the proof. |
| title | Non-trivial smooth families of $K3$ surfaces |
| topic | Differential Geometry Geometric Topology 57K41, 57R50 |
| url | https://arxiv.org/abs/2102.06354 |