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--- blog:2023-09-07 [2023/09/07 19:10] – created pzhou
+++ blog:2023-09-07 [2023/09/07 19:43] (current) – pzhou
@@ Line 17: / Line 17: @@
 I don't know how I get it, I guessed it, and it worked.
-So, we have local coordinates, and we have holomorphic symplectic form. (why it is non-degenerate?)
+So, we have local coordinates, and we have holomorphic symplectic form. (why it is non-degenerate? well, just check it locally. )
+We define $\omega_\theta = Re(e^{i\theta} \Omega)$.
+What does extra grading mean? Well, you can have if you have a Kahler manifold $M$, you can have $H^*(M)$ equipped with an extra grading $p-q$, Hodge grading. Is it possible to get this from the $S^1$-family? In the case of $\P^n$, all the weight grading are zero, because you only have $(i,i)$ class. That's not the case for elliptic curve, where you have $(1,0)$ and $(0,1)$.