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SUMMARY:Low-degree rational curves on quasi-polarized K3-surfaces
DTSTART:20231207T093000Z
DTEND:20231207T113000Z
DTSTAMP:20260504T201300Z
UID:indico-event-10923@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sławomir Rams\n\nThe study of configurations of rat
 ional curves on various surfaces has a long history. In the case of K3 sur
 faces one can mention Bogomolov and Mumford's proof of the fact that every
  complex projective K3 surface contains a (possibly singular) rational cur
 ve\, and fairly recent result by Chen\, Gounelas and Liedtke on the existe
 nce of infinitely many rational curves on every K3 surface over an algebra
 ically closed field of characteristic zero.The problem of rational curves 
 assumes a different flavour when we consider   quasi-polarized K3 surface
 s of a fixed degree h  (i.e. pairs (X\,H)\, such that the Picard divisor 
 H is big\, nef\, base-point free and non-hyperelliptic with self-intersect
 ion h) and take the degrees of the rational curves relative to the  polar
 ization H into account. In my talk  I will present some upper bounds on t
 he number of low degree rational curves on quasi-polarized K3  surfaces. 
 In particular\, if time allows me\, I will sketch the proof of the fact th
 at a complex projective K3 quartic with non-empty singular locus contains 
 at most 52 lines (a sharp bound\, joint work with A. Degtyarev (Ankara)) .
   \n\nhttps://indico.math.cnrs.fr/event/10923/
URL:https://indico.math.cnrs.fr/event/10923/
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