arXiv research

Uniformizes varieties with log-canonical singularities using ball quotients.

We prove the Yau-Tian-Donaldson's conjecture for any $\mathbb{Q}$-Fano variety that has a log smooth resolution of singularities such that the discrepancies of all exceptional divisors are non-positive. In other words, if such a Fano variety is K-polystable, then it admits a Kähler-Einstein metric. This extends the pre…

Study Kähler-Einstein potentials on stable varieties near singularities

We determine an explicit presentation by generators and relations of the cohomology algebra $H^*(\mathbb P^2\setminus C,\mathbb C)$ of the complement to an algebraic curve $C$ in the complex projective plane $\mathbb P^2$, via the study of log-resolution logarithmic forms on $\mathbb P^2$. As a first consequence, we de…

New non-Kähler 3-folds constructed via log conifold transitions.

Proves a Baum--Bott formula for foliations by curves with logarithmic terms.