We analyze the configurations of conics and lines on a special class of Kummer octic surfaces.In particular,we bound the number of conics by 176 and show that there is a unique surface with 176 conics,all irreducible:it admits a faithful action of one of the Mukai groups.Therefore,we also discuss conics and lines on Mukai surfaces:we discover a double plane(ramified at a smooth sextic curve)that contains 8,910 smooth conics.
K3-surfaceoctic surfaceKummer surfaceconicMukai group
Alex Degtyarev
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Department of Mathematics,Bilkent University,Ankara 06800,Turkey
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