## Speaker:

**Stephen Coughlan**

## Title:

**Elliptic Gorenstein projection**

## Abstract:

The archetype elliptic Gorenstein singularity on a $3$-fold
is the vertex of the affine cone over a K3 surface.
Given a family of $3$-folds of general type, in good cases
one may be able to degenerate to a 3-fold with an elliptic
Gorenstein singularity, and then project away from this
point to a $3$-fold of general type in a smaller ambient projective space.
Used in reverse, this resembles Fano's famous strategy for
constructing Fano $3$-folds whose anticanonical embedding is
in high codimension: construct the image of some projection
and then undo the projection.
As ever, the more subtle phenomena begin to arise
in codimension $4$, when we try to write $X$ in weighted $\mathbb{P}^7$.

This is joint work with Gavin Brown at Loughborough.