Spezielle Quotientensingularität/E8/Funktionenkörper/Polynome/Aufgabe/Lösung

Es ist

${}{\begin{aligned}P^{2}+Q^{3}+R^{5}&={\left({\frac {-U^{15}}{(1+V)^{7}V^{3}}}\right)}^{2}+{\left({\frac {-U^{10}}{(1+V)^{5}V^{2}}}\right)}^{3}+{\left({\frac {-U^{6}}{(1+V)^{3}V}}\right)}^{5}\\&={\frac {U^{30}}{(1+V)^{14}V^{6}}}+{\frac {-U^{30}}{(1+V)^{15}V^{6}}}+{\frac {-U^{30}}{(1+V)^{15}V^{5}}}\\&={\frac {U^{30}}{(1+V)^{14}V^{5}}}{\left({\frac {1}{V}}-{\frac {1}{(1+V)V}}-{\frac {1}{1+V}}\right)}\\&={\frac {U^{30}}{(1+V)^{14}V^{5}}}\cdot {\frac {1+V-1-V}{(1+V)V}}\\&=0.\end{aligned}}$

Zur gelösten Aufgabe