BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ben Church (Stanford) DTSTART:20260603T230000Z DTEND:20260604T000000Z DTSTAMP:20260604T125032Z UID:UCSD_NTS/152 DESCRIPTION:Title: Non-unirationality of surfaces and moduli spaces in positive characteri stic\nby Ben Church (Stanford) as part of UCSD number theory seminar\n \nLecture held in APM 7321.\n\nAbstract\nA variety is unirational if it ad mits a dominant rational map from projective space. In characteristic zero \, global tensor forms obstruct unirationality. This is the principle behi nd the Harris–Mumford theorem (1982): M_g is of general type\, and a for tiori not unirational\, for g large. In positive characteristic the pictur e is far wilder\, owing to the existence of inseparable maps\, and as a re sult the unirationality of only a handful of moduli spaces is understood.\ n\nI will introduce new techniques for obstructing unirationality in posit ive characteristic\, inspired by methods for proving hyperbolicity in comp lex geometry. As applications\, I give a counterexample to Shioda's 1977 c onjecture that a simply connected surface in positive characteristic is un irational if and only if it is supersingular. I also show that many Hilber t modular varieties in positive characteristic are not unirational or even covered by rational or elliptic curves.\n\npre-talk at 3pm\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/152/ END:VEVENT END:VCALENDAR