On the Kaehler metrics over ${mathrm{Sym}^{d}(X)$
| Autor: | Aryasomayajula, Anilatmaja, Biswas, Indranil, Morye, Archana S., Sengupta, Tathagata |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.geomphys.2016.08.002 |
| Popis: | Let $X$ be a compact connected Riemann surface of genus $g$, with $g \geq 2$. For each $d <\eta(X)$, where $\eta(X)$ is the gonality of $X$, the symmetric product $\text{Sym}^d(X)$ embeds into $\text{Pic}^d(X)$ by sending an effective divisor of degree $d$ to the corresponding holomorphic line bundle. Therefore, the restriction of the flat K\"ahler metric on $\text{Pic}^d(X)$ is a K\"ahler metric on $\text{Sym}^d(X)$. We investigate this K\"ahler metric on $\text{Sym}^d(X)$. In particular, we estimate it's Bergman kernel. We also prove that any holomorphic automorphism of $\text{Sym}^d(X)$ is an isometry. Comment: Final version; to appear in Journal of Geometry and Physics |
| Databáze: | arXiv |
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