Dominik Burek

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20172026

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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…