Seminarraum 00.003

## Seminar Algebra and Geometry: Erik Paemurru (University of Loughborough)

**Birational models of terminal sextic double solids**

It is known that quasismooth 3-fold Fano hypersurfaces with index 1 in weighted projective spaces over ℂ are birationally rigid (not birational to any other Fano 3-folds, conic bundles or del Pezzo fibrations). But very little is known when they carry non-orbifold singularities. I consider sextic double solids, one of the simplest such 3-folds, which have an isolated cA_n singularity. I have shown that n is at most 8, and that rigidity fails for n > 3. In this talk, I will illustrate this phenomenon by giving some examples.

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