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Yuri G. Prokhorov

Publications and source records attributed to Yuri G. Prokhorov.

17 recordsLinked to original sources
arXiv2009

Rationality of Three-Dimensional Quotients by Monomial Actions

Let $G$ be a finite 2-group and $K$ be a field satisfying that (i) $\fn{char}K\ne 2$, and (ii) $\sqrt{a}\in K$ for any $a\in K$. If $G$ acts on the rational function field $K(x,y,z)$ by monomial $K$-automorphisms, then the fixed field $K(x,y,z)^G$ is rational (= purely transcendental) over $K$. Applications of this theorem will be given.

math.AG↗
arXiv2002

On Zariski decomposition problem

We discuss different generalizations of Zariski decomposition, relations between them and connections with finite generation of divisorial algebras.

math.AG↗
arXiv2001

On log canonical thresholds, II

We prove that the only accumulation points of the set $T_3$ of all three-dimensional log canonical thresholds in the interval $[1/2,1]$ are $1/2+1/n$, where $n\in\ZZ$, $n\ge 3$.

math.AG↗
arXiv2000

On a conjecture of Shokurov: Characterization of toric varieties

We verify a special case of V. V. Shokurov's conjecture about characterization of toric varieties. More precisely, let $(X,D=\sum d_iD_i)$ be a three-dimensional log variety such that $K_X+D$ is numerically trivial and $(X,D)$ has only purely log terminal singularities. In this situation we prove the inequality \{center} $\sum d_i\le \rk\Weil(X)/(\operatorname{algebraic equivalence}) +\dim(X)$. \{center} We describe such pairs for which the equality holds and show that all of them are toric.

math.AG↗
arXiv1999

Boundedness of non-birational extremal contractions

We consider $K_X$-negative extremal contractions $f\colon X\to (Z,o)$, where $X$ is an algebraic threefold with only $ε$-log terminal Q-factorial singularities and $(Z,o)$ is a two (resp., one)-dimensional germ. The main result is that $K_X$ is 1, 2, 3, 4 or 6-complementary or we have, so called, exceptional case and then the singularity $(Z\in o)$ is bounded (resp., the multiplicity of the central fiber $f^{-1}(o)$ is bounded).

math.AG↗
arXiv1999

Blow-ups of canonical singularities

In this paper we apply Shokurov's inductive method to study terminal and canonical singularities. As an easy consequence of the Minimal Model Program we show that for any three-dimensional log terminal singularity there exists some special, so called, plt blow-up. We discuss properties of them and construct some examples.

math.AG↗