BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jihun Park (POSTECH) DTSTART:20200721T110000Z DTEND:20200721T120000Z DTSTAMP:20260423T052836Z UID:ZAG/33 DESCRIPTION:Title: Cay ley octads\, plane quartic curves\, Del Pezzo surfaces of degree 2 and dou ble Veronese cones\nby Jihun Park (POSTECH) as part of ZAG (Zoom Algeb raic Geometry) seminar\n\n\nAbstract\nA net of quadrics in the 3-dimension al projective space whose singular members are parametrized by a smooth pl ane quartic curve has exactly eight distinct base points\, called a regula r Cayley octad. It is a classical result that there is a one-to-one corr espondence between isomorphism classes of regular Cayley octads and isomor phism classes of smooth plane quartic curves equipped with even theta-char acteristics. We can also easily observe a one-to-one correspondence betwe en isomorphism classes of smooth plane quartic curves and isomorphism clas ses of smooth Del Pezzo surfaces of degree 2. In this talk\, we set up a o ne-to-one correspondence between isomorphism classes of smooth plane quart ic curves and isomorphism classes of double Veronese cones with 28-singula r points. Also\, we explain how the 36 even theta characteristics of a giv en smooth quartic curve appear in the corresponding double Veronese cone. This is a joint work with Hamid Ahmadinezhad\, Ivan Cheltsov and Constanti n Shramov.\n LOCATION:https://researchseminars.org/talk/ZAG/33/ END:VEVENT END:VCALENDAR