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)