Sixfolds of generalized Kummer type and K3 surfaces
| Autor: | Floccari, Salvatore |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Compositio Mathematica, Volume 160, Issue 2, February 2024, pp. 388 - 410 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/S0010437X23007625 |
| Popis: | We prove that any hyper-K\"{a}hler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm{K}3^{[3]}$-type. It is obtained as crepant resolution of the quotient of $K$ by a group of symplectic involutions acting trivially on its second cohomology. When $K$ is projective, the variety $Y_K$ is birational to a moduli space of stable sheaves on a uniquely determined projective~$\mathrm{K}3$ surface~$S_K$. As application of this construction we show that the Kuga-Satake correspondence is algebraic for the K3 surfaces $S_K$, producing infinitely many new families of $\mathrm{K}3$ surfaces of general Picard rank $16$ satisfying the Kuga-Satake Hodge conjecture. Comment: v3: final version, to appear in Compositio Mathematica |
| Databáze: | arXiv |
| Externí odkaz: |
|