Month:  Mar 2017 Apr 2017 May 2017 Jun 2017 Jul 2017 Aug 2017 Sep 2017 Oct 2017 Nov 2017 Dec 2017 Jan 2018 Feb 2018 Mar 2018 Apr 2018 May 2018 Jun 2018 Jul 2018 Aug 2018 Sep 2018 Oct 2018 Nov 2018 Dec 2018 Jan 2019 Feb 2019 Mar 2019 Week:  Aug 14 - Aug 18 Aug 21 - Aug 25 Aug 28 - Sep 1 Sep 4 - Sep 8 Sep 11 - Sep 15 Sep 18 - Sep 22 Sep 25 - Sep 29 Oct 2 - Oct 6 Oct 9 - Oct 13 Oct 16 - Oct 20 Oct 23 - Oct 27 Oct 30 - Nov 3 Nov 6 - Nov 10 Nov 13 - Nov 17 Nov 20 - Nov 24 Year:  2015 2016 2017 2018 2019 2020 2021 2022 Login
Friday, September 22, 2017
Public Access

Category:
Category: All

22
September 2017
Mon Tue Wed Thu Fri Sat Sun
1 2 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
8:00am [3:30pm]Prof. M. S. Raghunathan Description: Title: Kodaira's theorem: criterion for embedding a compact Kahler manifold in projective space Abstract: Let $M$ be a compact Kahler manifold and $\Omega (M)$ the canonical $2$-form on $M$. When $M$ is projective $n$-spce $\P^n(\C)$ , $H^2(M,\C)$ is of dimension 1. It follows that for any Kahler metric on the projective space, the cohomology class $[\Omega (M)$ of the canonical $2$-form is a multiple of the (unique up to sign) of a generator of $H^2(M,\Z)$. It is immediate from this that if $M$ is a complex sub-manifold of $\P^n(\C)$ for some $n$, then for the Kahler metric on $M$ induced from one on $\P^n(\C)$, it is clear that $[\Omega(M)] \in$\C \cdot H^2(M, Z)$. Kodaira's theorem is a converse to this fact: If a complex manifold$M$admits a Kahler metric such that the class of$\Omega(M)$is a multiple of an integral class, then$M\$ can be embedded in some projective space. This result was conjectured by W V D Hodge.