Unirationality of certain supersingular $K3$ surfaces in characteristic 5
We show that every supersingular K3 surface in characteristic 5 with Artin invariant less than or equal to 3 is unirational.
math.AG↗
arXiv subjects
Duc Tai Pho
Publications and source records attributed to Duc Tai Pho.
Classification of sextics of torus type
The second author classified configurations of the singularities on tame sextics of torus type. In this paper, we give a complete classification of the singularities on irreducible sextics of torus type, without assuming the tameness of the sextics. We show that there exists 121 configurations and there are 5 pairs and a triple of configurations for which the corresponding moduli spaces coincide, ignoring the respective torus decomposition.
math.AG↗
Fundamental group of sextics of torus type
We show that the fundamental group of the complement of any irreducible tame torus sextics in $\bf P^2$ is isomorphic to $\bf Z_2*\bf Z_3$ except one class. The exceptional class has the configuration of the singularities $\{C_{3,9},3A_2\}$ and the fundamental group is bigger than $\bf Z_2*\bf Z_3$. In fact, the Alexander polynomial is given by $(t^2-t+1)^2$. For the proof, we first reduce the assertion to maximal curves and then we compute the fundamental groups for maximal tame torus curves.
math.AG↗