Bilinkage in codimension $3$ and canonical surfaces of degree $18$ in ${\mathbb{P}}^5$

Abstract

We study the behavior of the bilinkage process in codimension $3$. In particular, we construct a smooth canonically embedded and linearly normal surface of general type of degree $18$ in ${\mathbb{P}}^5$, this is probably the highest degree such surface may have. Next, we apply our construction to find a geometric description of Tonoli Calabi--Yau threefolds in ${\mathbb{P}}^6$.

16 pages, Annali della Scuola Normale di Pisa - Classe di Scienze 2015

References in corpus (4)

• Analysis on some infinite modules, inner projection, and applications
• Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections
• Calabi--Yau threefolds in ${\mathbb{P}}^6$
• Implementing the Kustin-Miller complex construction