arXiv subjects

Sokratis Zikas

Publications and source records attributed to Sokratis Zikas.

6 recordsLinked to original sources

arXiv2025

On Mori dreamness of blowups along space curves

We study the problem of determining when the blowup $X \to \mathbb{P}^3$ along a smooth space curve $C$ is a Mori Dream Space. We obtain sufficient conditions, as well obstructions to the Mori dreamness of $X$ based on the external geometry of $C$. We furthermore find infinitely many pairs $(g,d)$ such that the corresponding Hilbert schemes $H_{g,d}^S$ admit components whose general element has these obstructions. As a consequence we show that Mori dreamness is not an open property in flat families and exhibit various degenerational pathologies.

math.AG↗

arXiv2024

On Gizatullin's Problem for quartic surfaces of Picard rank $2$

In this paper we determine which automorphisms of general smooth quartic surfaces $S\subset \mathbb{P}^3$ of Picard rank $2$ are restrictions of Cremona transformations of $\mathbb{P}^3$.

math.AG↗

arXiv2024

Umemura Quadric Fibrations and Maximal Subgroups of $Cr_n(\mathbb{C})$

We study the equivariant geometry of special quadric fibrations, called Umemura quadric fibrations, as well as the maximality of their automorphism groups inside $Cr_n(\mathbb{C})$. We produce infinite families of pairwise non-conjugate maximal connected algebraic subgroups of $Cr_n(\mathbb{C})$.

math.AG↗

arXiv2023

Sarkisov Links with centres space curves on smooth cubic surfaces

We construct and study Sarkisov links obtained by blowing up smooth space curves lying on smooth cubic surfaces. We restrict our attention to the case where the blowup is not weak Fano. Together with the results of arXiv:1106.3716 which cover the weak Fano case, we provide a classification of all such curves. This is achieved by computing all curves which satisfy certain necessary criteria on their multisecant curves and then constructing the Sarkisov link step by step.

math.AG↗

arXiv2023

Rigid birational involutions of $\mathbb{P}^3$ and cubic threefolds

We construct families of birational involutions on $\mathbb{P}^3$ or a smooth cubic threefold which do not fit into a non-trivial elementary relation of Sarkisov links. As a consequence, we construct new homomorphisms from their group of birational transformations, effectively re-proving their non-simplicity. We also prove that these groups admit a free product structure. Finally, we produce automorphisms of these groups that are not generated by inner and field automorphisms.

math.AG↗

arXiv2022

Connected algebraic subgroups not lying in a maximal one

We prove that for each $n \geq 2$, there exists a ruled variety X of dimension n such that Bir(X) contains connected algebraic subgroups which are not lying in a maximal one.

math.AG↗