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SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20260417T124000Z
DTEND:20260417T134000Z
DTSTAMP:20260423T034446Z
UID:OBAGS/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/84/">A
  decade of line counting: an overview</a>\nby Alexander Degtyarev (Bilkent
 ) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nI wil
 l give a brief overview of a long project that started a decade ago (in\nc
 ollaboration with Ilia Itenberg and Sinan Sert\\"oz and in parallel with\n
 S{\\l}awomir Rams and Matthias Sch\\"utt) and originally intended to bridg
 e a minor\ngap in the proof of Segre's celebrated theorem on 64 lines on a
  smooth\nquartic surface. Confining ourselves to polarized K3-surfaces\, n
 ow we manage\nto answer questions that no one even dared to ask\, mostly b
 ecause of lack of\ntools. For example\, we \n\n$\\bullet$\nobtained sharp 
 upper bounds on the possible number of lines on a smooth polarized\nK3-sur
 face of any degree\,\n\n$\\bullet$ obtained similar bounds for quartics\, 
 sextics\, and octics with singularities\,\n\n$\\bullet$ advanced in the un
 derstanding of conics on K3-surfaces\,\n\n\n$\\bullet$ started the study o
 f twisted cubics.\n \n\nI will try to discuss both classical (more than 5 
 years old) results\nand recent advances\; if time permits\, I will also tr
 y to outline the\ntechniques used.\n
LOCATION:https://researchseminars.org/talk/OBAGS/84/
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