Timeline for All Kähler metrics on a complex manifold?
Current License: CC BY-SA 3.0
6 events
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| Oct 24, 2017 at 21:00 | comment | added | user21574 | ....Now I give relative version of pervious comment: suppose that $\mathcal X\to S$ be a holomorphic surjective map of Kahler manifolds and $\mathcal L$ be a relatively ample line bundle over $\mathcal X$. Now denote $\mathcal K_{\mathcal L/S}$ be the space of all Kahler metrics $\omega$ on $\mathcal L$ with positive curvature such that its restriction on each fiber $\mathcal X_s$, we have $\omega_s\in c_1(\mathcal L_s)$ then $\mathcal K_{\mathcal L/S}$ is an infinite dimensional fiber bundle over $S$ whose fibers are of the form $\mathcal H_L$ | |
| Oct 24, 2017 at 21:00 | comment | added | user21574 | Let $X$ be a Kahler manifolds and $L$ be an ample line bundle then if we denote $\mathcal H_L$ be the space of all Kahler metrics $\omega\in c_1(L)$, then we know $\mathcal H(L)\cong \frac{GL(N,\mathbb C)}{U(N)}$ | |
| Jul 26, 2017 at 4:19 | comment | added | user21574 | Given a family $f:X→S$ with singular central fibre $X_0$ and with generic fibre $X_s$ a Calabi-Yau variety, mirror symmetry produces, in some cases, a dual family $\tilde f:\tilde X→S$ satisfying certain properties. For instance, the moduli space of complex structures on $X_s$ is isomorphic to the complexified moduli space of Kähler structures on $\tilde X_s$ and vice versa. | |
| Jul 4, 2017 at 22:59 | history | edited | user21574 | CC BY-SA 3.0 |
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| Jul 4, 2017 at 22:54 | history | edited | user21574 | CC BY-SA 3.0 |
added 344 characters in body
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| Jul 4, 2017 at 22:35 | history | answered | user21574 | CC BY-SA 3.0 |