4 papers
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 has the Lehmer property if divides where is an Euler totient function. In this note we shall prove that if 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…