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Counting lines on quartic surfaces: new techniques and results

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Davide Cesare Veniani (Hannover)

What
  • SFB-Kolloquium
When Jan 28, 2016
from 01:00 pm to 02:00 pm
Where Mainz, 05-432 (Hilbertraum)
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Abstract.

In the last years, two independent research teams (the one based in Ankara, Turkey, the other in Hannover, Germany) have tackled the problem of counting lines on smooth quartic surfaces; the former aimed at a complete classification using computer algebra system GAP, the latter strove for more geometrical insight.

The synergy between the two methods has fostered new ideas towards three goals: (1) finding a proof of the fact that the maximal number of lines is 64 which does not involve the flecnodal divisor; (2) proving the uniqueness of the surface with 64 lines with a geometrical approach; (3) adapting the methods to the K3 quartic case.

I will report about the state of the art.