BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sho Tanimoto (Kumamoto University) DTSTART:20201215T110000Z DTEND:20201215T120000Z DTSTAMP:20260423T021230Z UID:ZAG/77 DESCRIPTION:Title: Rat ional curves on Fano threefolds\nby Sho Tanimoto (Kumamoto University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nMori prov ed that a smooth Fano variety contains a lots of rational curves using fam ous Bend and Break technique. Thus it is natural to study the space of rat ional curves on a smooth Fano variety. Lines and conics on Fano threefolds are well studied\, and one may ask what one can say about higher degree r ational curves. Recently we established Movable Bend and Break for Fano th reefolds claiming that any free curve of high degree breaks into the union of two free curves. A proof is intricate\, and it relies on many properti es of three dimensional MMP such as Mori’s classification of divisorial contractions on smooth projective threefolds. In this talk I would like to explain some aspects of our proof of Movable Bend and Break as well as an application to Batyrev’s conjecture predicting a polynomial growth of t he number of components of bounded degree for the moduli space of rational curves. If time permits\, then I also explain a relation of our study to Geometric Manin’s conjecture which is an inspiration of our study. This is joint work with Roya Beheshti\, Brian Lehmann\, and Eric Riedl.\n LOCATION:https://researchseminars.org/talk/ZAG/77/ END:VEVENT END:VCALENDAR