University of Cambridge > > Algebraic Geometry Seminar > Z/2Z-equivariant smoothings of cusp singularities

Z/2Z-equivariant smoothings of cusp singularities

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If you have a question about this talk, please contact Dhruv Ranganathan.

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.

This talk is part of the Algebraic Geometry Seminar series.

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