Dominik Burek

activity

20172026

collaborators

10 papers

math.AG2026

Crepant resolutions of four-dimensional finite quotients

Dominik Burek, Sławomir Cynk

We give counterexamples to the conjecture of Dais-Henk-Ziegler on projective crepant resolutions of complete-intersection quotient singularities. For finite $G\subset\operatorname{…

math.AG2026

An elliptic Calabi-Yau threefold of Mordell-Weil rank twelve

Dominik Burek

We construct a smooth projective Calabi-Yau threefold with a flat elliptic fibration of Mordell-Weil rank twelve and Hodge numbers $(h^{1, 1}, h^{2, 1}) = (25, 1)$ . The construction star…

math.AG2026

Crepant resolutions of fiber products and Kummer fibrations of rational elliptic surfaces with non-reduced fibers

Dominik Burek, Sławomir Cynk

Let $S_{1}$ and $S_{2}$ be rational elliptic surfaces with section over an algebraically closed field of characteristic zero, and let $X = S_{1} \times_{P^{1}} S_{2}$ . We determine the…

math.AG2023

Fixed-locus relations and purely non-symplectic automorphisms of order 6 on K3 surfaces

Dominik Burek

We study relations between invariants of the fixed loci of purely non-symplectic automorphisms of $K 3$ surfaces. We obtain these relations by comparing the stringy Euler characteri…

math.AG2021

Zeta function of some Kummer Calabi-Yau 3-folds

Dominik Burek

We compute Hodge numbers and zeta function of a Kummer Calabi-Yau 3-folds introduced by M. Andreatta and J. Wiśniewski in arXiv:0804.4611 and investigated by M. Donten-Bury in arXi…

math.AG2021

Higher dimensional analogon of Borcea-Voisin Calabi-Yau manifolds, their Hodge numbers and $L$ -functions

Dominik Burek

We construct a series of examples of Calabi-Yau manifolds in an arbitrary dimension and compute the main invariants. In particular, we give higher dimensional generalization of Bor…

math.AG2018

Higher dimensional Calabi-Yau manifolds of Kummer type

Dominik Burek

Based on Cynk-Hulek method we construct complex Calabi-Yau varieties of arbitrary dimensions using elliptic curves with automorphism of order 6. Also we give formulas for Hodge num…

math.NT2018

A new upper bound for numbers with the Lehmer property and its application to repunit numbers

Dominik Burek, Błażej Żmija

A composite positive integer $n$ has the Lehmer property if $ϕ (n)$ divides $n - 1,$ where $ϕ$ is an Euler totient function. In this note we shall prove that if $n$ has the Lehmer pro…

math.AG2017

Rigid realizations of modular forms in Calabi--Yau threefolds

Dominik Burek

We construct examples of modular rigid Calabi--Yau threefolds, which give a realization of some new weight 4 cusp forms.

math.AG2017

Hodge Numbers of Generalised Borcea-Voisin Threefolds

Dominik Burek

We shall reproof formulas for the Hodge numbers of Calabi-Yau threefolds of Borcea-Voisin type constructed by A. Cattaneo and A. Garbagnati, using the orbifold cohomology formula a…

Crepant resolutions of four-dimensional finite quotients

An elliptic Calabi-Yau threefold of Mordell-Weil rank twelve

Crepant resolutions of fiber products and Kummer fibrations of rational elliptic surfaces with non-reduced fibers

Fixed-locus relations and purely non-symplectic automorphisms of order 6 on K3 surfaces

Zeta function of some Kummer Calabi-Yau 3-folds

Higher dimensional analogon of Borcea-Voisin Calabi-Yau manifolds, their Hodge numbers and L-functions

Higher dimensional Calabi-Yau manifolds of Kummer type

A new upper bound for numbers with the Lehmer property and its application to repunit numbers

Rigid realizations of modular forms in Calabi--Yau threefolds

Hodge Numbers of Generalised Borcea-Voisin Threefolds

Higher dimensional analogon of Borcea-Voisin Calabi-Yau manifolds, their Hodge numbers and $L$ -functions