arXiv research

Policy-gradient method controls multiple non-cohesive targets.

The paper constructs exotic complex projective surfaces using rational blowdowns.

Corrects a flawed proof of the Kropholler Conjecture.

We algebraically prove K-stability of polarized Calabi-Yau varieties and canonically polarized varieties with mild singularities. In particular, the} "stable varieties" introduced by Kollar-Shepherd-Barron and Alexeev, which form compact moduli space, are proven to be K-stable although it is well known that they are \t…

Study wormholes in surface moduli space, proving conjecture.

We construct a simply connected minimal complex surface of general type with $p_g=0$ and $K^2=2$ which has an involution such that the minimal resolution of the quotient by the involution is a simply connected minimal complex surface of general type with $p_g=0$ and $K^2=1$. In order to construct the example, we combin…

We describe and document three mechanisms by which corporations can influence or even control stock prices. (i) Parent and holding companies wield control over other publicly traded companies. (ii) Through clever management of treasury stock based on buyback programs and stock issuance, stock price fluctuations can be …

Classifies surfaces with T-singularities and ample canonical class.

For projective varieties with definite first Chern class we have one type of canonical metric which is called Kähler-Einstein metric. But for varieties with an intermidiate Kodaira dimension we can have several different types of canonical metrics. In this paper we introduce a new notion of canonical metric for varieti…

We introduce a new unsupervised anomaly detection ensemble called SPI which can harness privileged information - data available only for training examples but not for (future) test examples. Our ideas build on the Learning Using Privileged Information (LUPI) paradigm pioneered by Vapnik et al. [19,17], which we extend …

Let $X$ be a canonically polarized variety, i.e. a complex projective variety such that its canonical class $K_{X}$ defines an ample $\Q-$line bundle, and satisfying the conditions $G_1$ and $S_2$. Our main result says that $X$ admits a Kähler-Einstein metric iff $X$ has semi-log canonical singularities i.e. iff $X$ is…