Graduate School of Mathematics, Nagoya University
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Update: 2018/10/21


Detail of Seminar

Created: 2018/09/27, Modified: 2018/09/27
Subject Algebraic Geometry Seminar
Speaker(s) Yuya Matsumoto (Tokyo University of Science)
Title μp- and αp-actions on K3 surfaces in characteristic p
2018/10/15 13:00–14:30
Place Science Bldg. A, Room 207

We consider μp- and αp-actions on RDP K3 surfaces (K3 surfaces with rational double point singularities allowed) in characteristic p>0.
We focus on actions whose quotients are also RDP K3 surfaces, and we determine the possible configuration of singularities.
The results are parallel to the cases of Z/lZ- and Z/pZ-quotients.
Then we show that conversely an RDP K3 surface with a certain configuration of singularities admits a μp- or αp-covering by a surface, which is often an RDP K3 surface but not always(cf: the covering of an Enriques surface in characteristic 2).
As a by-product we prove that certain RDPs, for example D81 in characteristic 2, cannot occur on RDP K3 surfaces.