Tuesday, December 19, 2017 - 13:15
HU, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 3.006, Erdgeschoss
Forschungsseminar "Arithmetische Geometrie"
Prof. J. Kramer, Prof. Th. Krämer
The number of lines on a smooth complex surface in projective space depends very much on the degree of the surface. Planes and conics contain infinitely many lines and cubics always have exactly 27. As for degree 4, a general quartic surface has no lines, but Schur's quartic contains as many as 64. This is indeed the maximal number, but a correct proof of this fact was only given quite recently. Can a quartic surface carry exactly 63 lines? How many can there be on a quartic which is not smooth, or which is defined over a field of positive characteristic? In the last few years many of these questions have been answered, thanks to the contribution of several mathematicians. I will survey the main results and ideas, culminating in the list of the explicit equations of the ten smooth complex quartics with most lines.
submitted by Kristina Schulze (schulze@math.hu-berlin.de)