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i have a question to determin if the asyptotic expansion of Bergman kernel has a log term. Is there anyone can show me is there any general way to tell?

Suppose we have a fibration over the punctured disc (i.e., a deformation of complex manifolds) such that each fiber is a homogeneous space. Is the total space a product of a fiber with the punctured d …

Can anyone write down the biholomorphic map between classical bounded symmetric domains(defiend by matrixs) with their siegel upperhalf plane models. I know if it's type 2, i.e $I-Z\bar{Z}^{t}>0$ whe …

I want to know the parallel properties of Douady space with respect to Hilbert scheme. For example I want to know what is the irreducible component of Douady space, what if I consider a family of fixe …

Suppose that $f \colon X\rightarrow S$ is a proper morphism of reduced and irreducible complex spaces and $f$ is a smooth deformation in the sense of Kodaira and Spencer. If we know each fiber $X_s$, …

I have a question on Hodge and Atiyah's paper "Integrals of the second kind on an algebraic variety". It is about the exact sequence below formula (14) and above formula (15) on page 71: $$H_{2n-q}(S …

I am confused about the following question. Consider $\mathbb C^4$ endowed with nondegenerate symmetric bilinear form $J:=\left(\begin{matrix}0&0&0&1\\0&0&1&0\\0&1&0&0\\1&0&0&0\end{matrix}\right)$. L …