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Blowing down noncommutative cubic surfaces

Recent Developments in Noncommutative Algebraic Geometry April 08, 2024 - April 12, 2024

April 11, 2024 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Shinnosuke Okawa (Osaka University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Blowing down noncommutative cubic surfaces


In 2001 Van den Bergh defined the notion of blowup for noncommutative surfaces and showed that the blowup of a noncommutative P2 in 6 points is isomorphic to a cubic surface inside a noncommutative P3. This yields a rational map from the moduli space of noncommutative P2s equipped with 6 points to a component of the moduli space of noncommutative P3s. In this talk I will show that the abstractly defined map as such turns out to be the composition of some concrete maps. This has various consequences, including the blowdown theorem. This is a joint work in progress with Ingalls, Sierra, and Van den Bergh.

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Blowing down noncommutative cubic surfaces

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