BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lei Yang (Northeastern University) DTSTART:20201012T200000Z DTEND:20201012T210000Z DTSTAMP:20260423T035910Z UID:AGSAGS/11 DESCRIPTION:Title: Cox rings\, linear blow-ups and the generalized Nagata action\nby Lei Yang (Northeastern University) as part of American Graduate Student Algebr aic Geometry Seminar\n\n\nAbstract\nNagata gave the first counterexample t o Hilbert's 14th problem on the finite generation of invariant rings by ac tions of linear algebraic groups. His idea was to relate the ring of invar iants to a Cox ring of a projective variety. Counterexamples of Nagata's t ype include the cases where the group is $G_a^m$ for $m=3\, 6\, 9$ or $13$ . However\, for $m=2$\, the ring of invariants under the Nagata action is finitely generated. It is still an open problem whether counterexamples ex ist for $m=2$. \n\nIn this talk we consider a generalized version of Nagat a's action by H. Naito. Mukai envisioned that the ring of invariants in th is case can still be related to a cox ring of certain linear blow-ups of $ P^n$. We show that when $m=2$\, the Cox rings of this type of linear blow- ups are still finitely generated\, and we can describe their generators. T his answers the question by Mukai.\n LOCATION:https://researchseminars.org/talk/AGSAGS/11/ END:VEVENT END:VCALENDAR