Explicit families of $K3$ surfaces having real multiplication
| Autor: | Elsenhans, Andreas-Stephan, Jahnel, J��rg |
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| Rok vydání: | 2020 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2002.00233 |
| Popis: | For families of $K3$ surfaces, we establish a sufficient criterion for real or complex multiplication. Our criterion is arithmetic in nature. It may show, at first, that the generic fibre of the family has a nontrivial endomorphism field. Moreover, the endomorphism field does not shrink under specialisation. As an application, we present two explicit families of $K3$ surfaces having real multiplication by $\bbQ(\sqrt{2})$ and $\bbQ(\sqrt{5})$, respectively. |
| Databáze: | OpenAIRE |
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