BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Fatma Karaoğlu (Gebze Teknik) DTSTART:20221202T124000Z DTEND:20221202T134000Z DTSTAMP:20260423T021255Z UID:OBAGS/16 DESCRIPTION:Title: S mooth cubic surfaces with 15 lines\nby Fatma Karaoğlu (Gebze Teknik) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIt is w ell-known that a smooth cubic surface has 27 lines over an algebraically c losed field. If the field is not closed\, however\, fewer lines are possib le. The next possible case is that of smooth cubic surfaces with 15 lines. This work is a contribution to the problem of classifying smooth cubic su rfaces with 15 lines over fields of positive characteristic. We present an algorithm to classify such surfaces over small finite fields. Our classif ication algorithm is based on a new normal form of the equation of a cubic surface with 15 lines and less than 10 Eckardt points. The case of cubic surfaces with more than 10 Eckardt points is dealt with separately. Classi fication results for fields of order at most 13 are presented and a verifi cation using an enumerative formula of Das is performed. Our work is based on a generalization of the old result due to Cayley and Salmon that there are 27 lines if the field is algebraically closed.\n\n Smooth cubic surfa ces with 15 lines\n LOCATION:https://researchseminars.org/talk/OBAGS/16/ END:VEVENT END:VCALENDAR