BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hernán Iriarte DTSTART:20210602T133000Z DTEND:20210602T143000Z DTSTAMP:20260423T004134Z UID:Rega/17 DESCRIPTION:Title: Ge ometry of Higher Rank Valuations\nby Hernán Iriarte as part of RéGA (Réseau des étudiants en Géométrie Algébrique)\n\n\nAbstract\nIt is w ell known since before Zariski that the set of (equivalent classes) of val uations on the function field of an algebraic curve is in correspondence w ith the points of the curve. In higher dimensional varieties\, this pictur e gets more complicated: Not every valuation is divisorial\, there are val uations of different ranks and the geometry of the space of valuations hig hly depends on when you consider two valuations to be equal.\n\nInspired b y understanding the relationship between Okounkov bodies and the full rank valuation that defines them\, we developed tools to understand geometrica lly the space of full rank valuations on function fields of algebraic vari eties. \n\nThe approach will be through the study of valuations of a simpl e kind called higher rank quasi-monomial valuations. These valuations can be completely expressed in combinatorial terms: They are partial derivativ e operators on the dual cone complex of a simple normal crossing divisor. These led us to consider tangent cones of dual cone complexes\, which will play the role of skeleta in this context. In particular\, the space of al l higher rank valuations can be obtained as a limit of tangent cones of co ne complexes. This is joint work with Omid Amini.\n LOCATION:https://researchseminars.org/talk/Rega/17/ END:VEVENT END:VCALENDAR