# Mathematics Calendar

Wednesday, January 15, 2020 - 13:15

HU J. v. Neumann-Haus

Rudower Chaussee 25, 12489 Berlin -Adlershof, Raum 1.114

Forschungsseminar "Algebraische Geometrie"

Prof. G. Farkas / Prof. B. Klingler

Let \( (S,L) \) be a general
\( (d_1,d_2) \)-polarized abelian surfaces. The minimal geometric
genus of any curve in the linear system \( |L| \) is two and there
are finitely many curves of such genus. In analogy with Chen's
results concerning rational curves on K3 surfaces, it is natural to
ask whether all such curves are nodal. In the seminar I will prove
that this holds true if and only if \( d_2\) is not divisible by \(4\). In the cases where \(d_2\) is a multiple of \(4\), I will construct curves in \(|L|\) having a triple, \(4\)-tuple or \(6\)-tuple point, and show that these are the only types of unnodal singularities a genus \(2\) curve in \(|L|\) may acquire. This is joint work with A. L. Knutsen.

submitted by Désirée Dzomo (dzomoqud@math.hu-berlin.de, 5823)