BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Howard Nuer (Technion\, Israel Institute of Technology) DTSTART:20210624T110000Z DTEND:20210624T120000Z DTSTAMP:20260423T021449Z UID:ZAG/132 DESCRIPTION:Title: Th e cohomology of the general stable sheaf on a K3 surface\nby Howard N uer (Technion\, Israel Institute of Technology) as part of ZAG (Zoom Algeb raic Geometry) seminar\n\n\nAbstract\nLet X be a K3 surface of Picard rank one and degree 2n with ample generator H. Let M_H(v) be the moduli space of Gieseker semistable sheaves on X with Mukai vector v. In this talk\, we consider the weak Brill-Noether property for v\, namely that the general sheaf in M_H(v) has at most one nonzero cohomology group. We show that g iven any positive rank r\, there are only finitely many Mukai vectors of r ank r failing weak Brill-Noether over all K3 surfaces of Picard rank one. We discuss our algorithm for finding the potential counterexamples and dem onstrate the utility of our approach by discussing how we were able to cla ssify all such counterexamples up to rank 20 and calculate the cohomology of the general sheaf in each case. Moreover\, for fixed rank r\, we give sharp bounds on n\, d\, and a that guarantee that a Mukai vector v=(r\,dH\ ,a) satisfies weak Brill-Noether. As a corollary\, we provide another pro of of the classification of Ulrich bundles on K3 surfaces of Picard rank o ne. In addition\, we discuss the question of when the general sheaf in M_H (v) is globally generated. This joint work with Izzet Coskun and Kota Yosh ioka makes crucial use of Bridgeland stability conditions and wall-crossin g.\n LOCATION:https://researchseminars.org/talk/ZAG/132/ END:VEVENT END:VCALENDAR