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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

1 vote
0 answers
407 views

Finite generation of canonical ring in Geometric PDE

We say that a projective variety $X$ is of general type if the Kodaira dimension is equal to the dimension of $X$., i.e. $\text{kod}(X)=\dim X$. When $K_X$ is positive then by the result of S.T.Yau w …
9 votes
0 answers
291 views

Coarse moduli space of compact polarized Fano Kaehler-Einstein manifolds

Let $\mathcal X\to \mathcal S$, be a family of polarized Kaehler manifolds with $\omega_s= Ric(\omega_s)$(i.e., fibers are Fano Kahler-Einstein manifolds). Then $dim Aut(X_s)=Const$.? Is there any co …
11 votes
0 answers
295 views

Computing $h^1$ of dual of graph of central fibre of the degeneration of Kaehler-Einstein ma...

Consider a Kaehler degeneration $\mathcal X\to \Delta$ of smooth manifolds: Here $\Delta$ is the unit disc, $\pi$ a proper flat map, smooth over $\Delta^∗=\Delta−\{0\}$. The general fibres are $X_t=\ …
10 votes
1 answer
517 views

Zariski open subset on family of Kaehler-Einstein manifolds

Let $\pi:\mathcal X\to B$ be a family of Kaehler manifolds then if we take $B'\subset B$ be the set of parameters such that $X_b$ admit Kaehler-Einstein metric(with zero, negative, or positive Ricci c …