Canonical 3-folds in P^2 x P^2 format and numerical K3 transitions
Canonical 3-folds in $\mathbb{P}^2\times\mathbb {P}^2$ format and numerical $K3$ transitions
Siberian Electronic Mathematical Reports, 22, 2, pp. 1673-1686 (2025)
Abstract:
We provide a conjectural extension of the web of canonical 3-folds by proving the existence of some new deformation families of canonical 3-folds embedded in weighted projective space $\mathbb P^7(w_0,\ldots,w_7)$. These families can be presented by using the equations of Segre embedding of $\mathbb P^2\times \mathbb P^2$. We provide a table of candidate numerical $K3$ transitions that can relate these families to the existing web of canonical 3-folds.
Keywords: canonical 3-folds, weighted projective space, $\mathbb P^2\times \mathbb P^2$ format, K3 transitions.