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

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 ${\mathbb{P}}^6$.

25 pages, Annali di Matematica Pura ed Applicata 01.2015

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