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NumericalGodeaux :: lineConditionsTorsZ2

lineConditionsTorsZ2 -- compute a list of possible loci for Z/2Z-Godeaux surfaces

Synopsis

Description

The order of the torsion group does only depend on the choice of the line in the complete intersection of the quadratic relations $Q$ in $\mathbb{P}^{11}$. A numerical Godeaux surface $X$ with torsion group $\mathbb{Z}/2$ has a double bicanonical curve $2D_2$, where $D_2 \in |K_X + t_2|$ with a torsion element $t_2$ of order 2. To construct surfaces with such a curve, the chosen line in $Q$ must intersect a particular loci in $Q$ which is determined in this procedure.

Ways to use lineConditionsTorsZ2 :

For the programmer

The object lineConditionsTorsZ2 is a method function.