BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giancarlo Urzúa DTSTART:20200820T140000Z DTEND:20200820T150000Z DTSTAMP:20260423T052834Z UID:Freemath/16 DESCRIPTION:Title: On the geography of complex surfaces of general type with an arbitrary f undamental group\nby Giancarlo Urzúa as part of Free Mathematics Semi nar\n\n\nAbstract\nSurfaces of general type are lovely unclassifiable obje cts in algebraic geometry. Geography refers to the problem of construction of such surfaces for a given set of invariants\, classically the Chern nu mbers \\(c_1^2\\) (self-intersection of canonical class) and \\(c_2\\) (to pological Euler characteristic). In this talk\, we treat the question: Wha t can be said about the distribution of Chern slopes \\(c_1^2/c_2\\) of su rfaces of general type when we fix the fundamental group? It turns out tha t there are various well-known constraints\, which will be pointed out dur ing the talk\, but at least we can prove the following theorem (joint with Sergio Troncoso): "Let \\(G\\) be the fundamental group of some nonsingul ar complex projective variety. Then Chern slopes of surfaces of general t ype with fundamental group isomorphic to \\(G\\) are dense in the interval \\([1\,3]\\).". Remember that for complex surfaces of general type we hav e that \\(c_1^2/c_2\\) is a rational number in \\([1/5\,3]\\)\, and so mos t open questions now refer to slopes in \\([1/5\,1]\\). On the other hand\ , it is known that every finite group is the fundamental group of some non singular projective variety\, and so a lot is going on for high slopes.\n LOCATION:https://researchseminars.org/talk/Freemath/16/ END:VEVENT END:VCALENDAR