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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
2
answers
538
views
$dd^\mathbb{C}$-lemma on pair $(X,D)$
Let $X$ be a Kähler manifold with a simple normal crossing divisor $D$, i.e., pair $(X,D)$. Let $\omega$ and $\omega'$ be two Kähler forms in the same Kähler class then have we $dd^\mathbb{C}$-lemma o …
1
vote
1
answer
266
views
Moment map coordinates in tours action
I am trying to understand the proof of lemma 3.1, in this paper
In proof, they say that $g(dz_i,d\tau_k)=dz_i(\nabla\tau_k)=0$ I don't understand first and second equality.In second they say, $g(dz_i …
1
vote
1
answer
303
views
symplectic reduction for pair $(M,D)$
Let $M$ be a symplectic manifold with divisor $D$. Then how can we define symplectic reduction for pair $(M,D)$?