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New examples of modular rigid Calabi-Yau threefolds.

Matthias Schütt — 2004

Collectanea Mathematica

The aim of this article is to present five new examples of modular rigid Calabi-Yau threefolds by giving explicit correspondences to newforms of weight 4 and levels 10, 17, 21 and 73.

On the uniqueness of elliptic K3 surfaces with maximal singular fibre

Matthias Schütt; Andreas Schweizer — 2013

Annales de l’institut Fourier

We explicitly determine the elliptic $K 3$ surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from $2$ , for each of the two possible maximal fibre types, $I_{19}$ and $I_{14}^{*}$ , the surface is unique. In characteristic $2$ the maximal fibre types are $I_{18}$ and $I_{13}^{*}$ , and there exist two (resp. one) one-parameter families of such surfaces.

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