arXiv subjects

Daniil Serebrennikov

Publications and source records attributed to Daniil Serebrennikov.

3 recordsLinked to original sources

arXiv2026

Towards the Global Torelli Theorem

In this paper, we prove finiteness results for K-trivial varieties in all dimensions. In dimension 2, these results are corollaries of the Global Torelli Theorem for polarized K3 surfaces. In particular, we establish a sufficient condition when two fibers of a projective family of K-trivial varieties are isomorphic via the Hodge theory. As applications, we prove that if a projective family of K-trivial varieties has a dense subset of birationally equivalent fibers, then all fibers are isomorphic.

math.AG↗

arXiv2026

On the finiteness of log surfaces

We generalize the Kawamata-Matsuki conjecture to klt log pairs and prove it in dimension two. More precisely, we show that a log surface admits only finitely many weakly log canonical projective models with klt singularities up to log isomorphism, by reducing the problem to boundedness of polarizations.

math.AG↗

arXiv2026

Constructibility aspects of the cone conjecture

We establish two consequences of the Kawamata--Morrison--Totaro cone conjecture, and prove them unconditionally in all dimensions. First, for a K-trivial variety, the natural action of its automorphism group on the set of ample divisor classes of fixed volume has only finitely many orbits. Second, the number of (isomorphism classes of) minimal models for a given K-trivial variety is finite if these models admit a bounded polarization.

math.AG↗