Almost toric yoga for stable double surfaces (Part II)

Add to your list(s) Download to your calendar using vCal

• Jonny Evans (Lancaster)
• Friday 14 March 2025, 10:30-11:30
• CMS, MR15.

If you have a question about this talk, please contact Ailsa Keating.

Please note the unusual time and place.

(This is part II of a series of two talks.)The moduli space of surfaces of general type has a natural compactification where the boundary points correspond to ``stable surfaces’’. If we restrict attention to surfaces which are branched double covers of certain simple surfaces (like the projective plane or a Hirzebruch surface) then singularities can develop in three ways: the branch curve can degenerate, or the base surface can degenerate, or the branch curve and the base surface can develop singularities at the same point. If the limit of the base surface is toric, one can use toric geometry to understand the stable limit of the double cover, but often degenerations of the plane or a Hirzebruch surface are only almost toric (in a precise sense). Thanks to work of Gross, Hacking and Keel, the same diagrammatic techniques that work for toric degenerations can be applied in this setting, and one can use this to get a full classification of normal stable surfaces for some components of the moduli space. I will explain how this works for octic double planes. This is based on joint work with Angelica Simonetti and Giancarlo Urzua.

This talk is part of the Differential Geometry and Topology Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR15
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Differential Geometry and Topology Seminar
• Hanchen DaDaDash
• Interested Talks
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.