Calabi-Yau threefolds in ${\mathbb{P}}^n$ and Gorenstein rings

Hal Schenck, Mike Stillman, Beihui Yuan

A projectively normal Calabi-Yau threefold $X\subseteq {\mathbb{P}}^n$ has an ideal $I_X$ which is arithmetically Gorenstein, of Castelnuovo-Mumford regularity four. Such ideals hav…