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SUMMARY:Lei Yang (Northeastern University)
DTSTART:20201102T171500Z
DTEND:20201102T181500Z
DTSTAMP:20260423T021706Z
UID:GASC/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GASC/6/">Cox
  rings\, linear blow-ups and the generalized Nagata action</a>\nby Lei Yan
 g (Northeastern University) as part of Geometry\, Algebra\, Singularities\
 , and Combinatorics\n\n\nAbstract\nNagata gave the first counterexample to
  Hilbert's 14th problem on the finite generation of invariant rings by act
 ions of linear algebraic groups. His idea was to relate the ring of invari
 ants to a Cox ring of a projective variety. Counterexamples of Nagata's ty
 pe include the cases where the group is $\\mathbb{G}_a^m$ for $m$ greater 
 than or equal to $3$. However\, for $m=2$\, the ring of invariants under t
 he Nagata action is finitely generated. It is still an open problem whethe
 r counterexamples exist for $m=2$.\n\nIn this talk we consider a generaliz
 ed version of Nagata's action by H. Naito. Mukai envisioned that the ring 
 of invariants in this case can still be related to a cox ring of certain l
 inear blow-ups of $\\mathbb{P}^n$. 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. This answers the question by Mukai.\n
LOCATION:https://researchseminars.org/talk/GASC/6/
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