The Simanca metric admits a regular quantization

Remarks on Mukai threefolds admitting $C^{*}$ action

We investigate geometric invariants of the one parameter family of Mukai threefolds that admit $\mathbb C^{*}$ action. In particular we find the invariant divisors in the anticanonical system, and thus establish a bound on the log canonical thresholds. Furthermore we find an explicit description of such threefolds in terms of the quartic associated to the variety-of-sum-of-powers construction. This yields that any such threefold admits an additional symmetry which anticommutes with the $\mathbb C^{*}$ action, a fact that was previously observed near the Mukai-Umemura threefold by Rollin, Siman…

关于到 $\mathbb C^n$ 的爆破中的全纯等距映射

On holomorphic isometries into blow-ups of $\mathbb C^n$

本文研究可全纯等距嵌入广义 Burns-Simanca 流形或 Eguchi-Hanson 流形的 Kähler-Einstein 流形，并证明这两个流形与任何齐性有界域均无关联。

Berezin quantization of homogeneous bounded domains

We prove that a homogeneous bounded domain admits a Berezin quantization.

无挠 CR 流形的量子化与约化

Quantization and reduction for torsion free CR manifolds

本文研究紧致无挠 CR 流形上的量子化与约化，证明在自然假设下群不变 Fourier-Szegő 投影算子有完全渐近展开，并当线丛张量幂足够大时量子化与约化可交换。

Finite TYCZ expansions and cscK metrics

Let $(M, g)$ be a Kaehler manifold whose associated Kaehler form $ω$ is integral and let $(L, h)\rightarrow (M, ω)$ be a quantization hermitian line bundle. In this paper we study those Kaehler manifolds $(M, g)$ admitting a finite TYCZ expansion. We show that if the TYCZ expansion is finite then $T_{mg}$ is indeed a polynomial in $m$ of degree $n$, $n=dim M$, and the log-term of the Szegö kernel of the disc bundle $D\subset L^*$ vanishes (where $L^*$ is the dual bundle of $L$). Moreover, we provide a complete classification of the Kaehler manifolds admitting finite TYCZ expansion either when …

The probabilistic vs the quantization approach to Kähler-Einstein geometry

In the probabilistic construction of Kähler-Einstein metrics on a complex projective algebraic manifold X - involving random point processes on X - a key role is played by the partition function. In this work a new quantitative bound on the partition function is obtained. It yields, in particular, a new direct analytic proof that X admits a Kähler-Einstein metrics if it is uniformly Gibbs stable. The proof makes contact with the quantization approach to Kähler-Einstein geometry.