BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pieter Belmans (University of Luxembourg) DTSTART:20211116T160000Z DTEND:20211116T170000Z DTSTAMP:20260423T004551Z UID:DerSem/32 DESCRIPTION:Title: The Hirzebruch isomorphism for exotic noncommutative surfaces\nby Piet er Belmans (University of Luxembourg) as part of Derived seminar\n\n\nAbst ract\nThe isomorphism between the first Hirzebruch surface and the blowup of the projective plane in a point is a well-known result\, due to Hirzebr uch. From a numerical classification of Grothendieck groups of rank 4 whic h behave like the Grothendieck group of a smooth projective surface we exp ect the existence of exotic noncommutative surfaces\, which are surfaces n ot obtained via deforming commutative surfaces. There exist two constructi ons: one as an asymmetric noncommutative P^1-bundle (due to de Thanhoffer- -Presotto)\, one as a fat point blowup (joint work with Presotto). I will explain how a Hirzebruch isomorphism for these two families of surfaces ex ists as an equivalence of (derived) categories\, and how this is related t o some very classical geometry of linear systems. This is joint work with Dennis Presotto and Michel Van den Bergh.\n LOCATION:https://researchseminars.org/talk/DerSem/32/ END:VEVENT END:VCALENDAR