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arXiv · 1306.5628

Calabi--Yau threefolds in $\mathbb{P}^6$

Grzegorz Kapustka·Michal Kapustka
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Abstract

We study the geometry of $3$-codimensional smooth subvarieties of the complex projective space. In particular, we classify all quasi-Buchsbaum Calabi--Yau threefolds in projective $6$-space. Moreover, we prove that this classification includes all Calabi--Yau threefolds contained in a possibly singular 5-dimensional quadric as well as all Calabi--Yau threefolds of degree at most $14$ in $\mathbb{P}^6$.

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Grzegorz Kapustka, Michal Kapustka. 2013-06-24. Calabi--Yau threefolds in $\mathbb{P}^6$. https://doi.org/10.1007/s10231-015-0476-0

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