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Seminars

Pathological phenomena on Du Val del Pezzo surfaces

Hold Date
2021-06-11 16:00〜2021-06-11 17:00
Place
Zoom
Object person
 
Speaker
Masaru Nagaoka, Kyushu University

Keel-Mckernan constructed a del Pezzo surface with seven A_1-singularities over an algebrically closed field of characteristic two, although Du Val del Pezzo surfaces cannot have more than six singularities in characteristic zero. Hence this example is not log liftable, in other words, the pair of its minimal resolution and the exceptional divisor is not liftable over the ring of Witt vectors. On the other hand, this example has several pathological phenomena in positive characteristic. In this talk, we give relations between non-log liftability of Du Val del Pezzo surfaces and pathological phenomena in positive characteristic. After that, we introduce how to classify Du Val del Pezzo surfaces with pathological phenomena by applying these relations. This is a joint work with Tatsuro Kawakami in University of Tokyo.