7 papers
Shifting local exponents of Picard-Fuchs operators
Tymoteusz Chmiel
We investigate the operation of shifting local exponents and study its effects on the monodromy representation of a one-parameter family of Calabi-Yau threefolds. The main result i…
Counterexample to Néron-Ogg-Shafarevich criterion for Calabi-Yau threefolds
Tymoteusz Chmiel, Marcin Oczko
For any prime we construct a Calabi-Yau threefold defined over a finite extension of such that every model of over $\operatorname{Spec}\mathcal{O}_…
Orphan Calabi-Yau threefold with arithmetic monodromy group
Tymoteusz Chmiel
We study monodromy groups of Picard-Fuchs operators of one-parameter families of Calabi-Yau threefolds without a point of Maximal Unipotent Monodromy (\emph{orphan operators}). We…
Koszul modules of Kac-Moody Lie algebras
Tymoteusz Chmiel
We introduce Koszul modules associated with (graded) Kac-Moody Lie algebras. We provide a precise criterion for when these modules are of finite length. As an exemplary application…
Periods of singular double octic Calabi-Yau threefolds and modular forms
Tymoteusz Chmiel, Sławomir Cynk
By the modularity theorem every rigid Calabi-Yau threefold has associated modular form such that the equality of -functions holds. In this case period in…
Coefficients of the monodromy matrices of one-parameter families of double octic Calabi-Yau threefolds at a half-conifold point
Tymoteusz Chmiel
Doran and Morgan have introduced certain rational basis for the monodromy group of the Picard-Fuchs operator of a hypergeometric family of Calabi-Yau threefolds. In this paper we c…
Computing period integrals of rigid double octic Calabi-Yau threefolds with Picard-Fuchs operator
Tymoteusz Chmiel
We present a method for numerical computation of period integrals of a rigid Calabi-Yau threefold using Picard-Fuchs operator of a one-parameter smoothing. Our method gives a possi…