Timeline for Automorphism group of a compact Kahler manifold
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2013 at 18:19 | comment | added | Đức Anh | interesting informations! Thank you very much. | |
| Mar 11, 2013 at 17:30 | comment | added | Ben McKay | I can't recall a precise reference, but I recall that there are holomorphic maps $X \to Y$ of compact Kaehler manifolds, with generic fiber a genus 2 compact Riemann surface but with finitely many fibers being reducible curves consisting of elliptic curves and Riemann spheres meeting at various points, and with $Y$ Kobayashi hyperbolic. If I am right about that, then every entire curve has image in those elliptic curves and Riemann spheres, and doesn't move. | |
| Mar 11, 2013 at 15:57 | comment | added | Đức Anh | Thank you very much. So the automorphism group may be bad (?) Btw, I would like to explain my motivation. Consider an entire curve $f\colon \mathbb{C}\to X.$ There is some place in $X$ where we can control the image of the curve. So, is there any way to perturbate the curve, or to move the curve in a reasonable way? | |
| Mar 11, 2013 at 15:54 | history | edited | Venkataramana | CC BY-SA 3.0 |
added 17 characters in body; added 15 characters in body
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| Mar 11, 2013 at 15:45 | comment | added | Robert Bryant | Ah, actually, a compact Riemann surface of genus $g=2$ is hyperelliptic, so it always has a nontrivial automorphism group. You should have written '$g\ge3$' in your answer. | |
| Mar 11, 2013 at 15:34 | history | answered | Venkataramana | CC BY-SA 3.0 |