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Wednesday 17 November 2021, 14:15-15:15
Z/2Z-equivariant smoothings of cusp singularities
- 👤 Speaker: Angelica Simonetti, Cambridge
- 📅 Date & Time: Wednesday 17 November 2021, 14:15 - 15:15
- 📍 Venue: CMS MR13
Abstract
Cusp singularities and their quotients by a suitable action of Z/2Z are among the surface singularities which appear at the boundary of the compactification of the moduli space of surfaces of general type due to Kollar, Shepherd-Barron and Alexeev.
Since only those singularities that admit a smoothing family occur at the boundary of this moduli space, it is useful to find nice conditions under which they happen to be smoothable.
We will describe a sufficient condition for a cusp singularity admitting a Z/2Z action to be equivariantly smoothable. In particular we will see it involves the existence of certain Looijenga (or anticanonical) pairs (Y,D) that admit an involution fixed point free away from D and that reverses the orientation of D.
Series This talk is part of the Algebraic Geometry Seminar series.
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