All Questions

I'm reading the book 'An Introduction to the Kahler-Ricci Flow' (Lecture Notes in Mathematics 2086). They discuss Bott-Chern cohomology on complex spaces: Let $X$ be a complex space(i.e. analytic ...

Let $(M,J)$ be a complex manifold, where $J$ is the integrable complex structure. Let $X$ be a holomorphic vector field on $M$ and let $\varphi_{t} : M\rightarrow M $ be its flow. Question: Is $\...

Suppose we have a real-valued smooth function on a complex torus: $$f: \mathbb{C}^n/(\mathbb{Z}+\sqrt{-1}\mathbb{Z})^n\longrightarrow\mathbb{R},$$ i.e., this $f$ is a real-valued smooth function on $\...

Let $(M,\omega)$ be a compact Kähler manifold. The boundary behavior of Kähler cone is very interesting; however,it's hard to understand. A fundamental result is due to Demailly and Paun: they ...

Consider an entire function $f : \mathbb{C} \rightarrow \mathbb{C}$! We search the function $$ g: (a,b) \rightarrow \mathbb{C},$$ which solves the following equation locally: $g'(t)=f(g(t))$ and $g(0)=...