BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Degtyarev (Bilkent U.) DTSTART:20230310T140000Z DTEND:20230310T150000Z DTSTAMP:20260423T021048Z UID:LAGARTOS/56 DESCRIPTION:Title: Singular real plane sextic curves without real points\nby Alex Degty arev (Bilkent U.) as part of (LAGARTOS) Latin American Real and Tropical G eometry Seminar\n\n\nAbstract\nIt is a common understanding that any reaso nable geometric question about\nK3-surfaces can be restated and solved in purely arithmetical terms\, by\nmeans of an appropriately defined homologi cal type. For example\, this works\nwell in the study of singular complex sextic curves or quartic surfaces\, as well as in that of smooth real ones . However\, when\nthe two are combined (singular real curves or surfaces)\ , the approach fails as\nthe obvious concept of homological type does not fully reflect the geometry.\nWe show that the situation can be repaired if the curves in question have\nempty real part or\, more generally\, have n o real singular points\; then\, one can\nindeed confine oneself to the hom ological types consisting of the exceptional\ndivisors\, polarization\, an d real structure. Still\, the resulting arithmetical\nproblem is not quite straightforward\, but we manage to solve it in the case\nof empty real pa rt.\nThis project was conceived and partially completed during our joint s tay at\nthe Max-Planck-Institut für Mathematik\, Bonn.\n LOCATION:https://researchseminars.org/talk/LAGARTOS/56/ END:VEVENT END:VCALENDAR