Quadrik/Glatt/Glatter Abschluss/Aufgabe

Es sei ${}C\subseteq {\mathbb {A} }_{\mathbb {C} }^{2}$ eine glatte Quadrik. Zeige, dass auch der projektive Abschluss

{}{\tilde {C}}\subseteq {\mathbb {P} }_{\mathbb {C} }^{2}\,

glatt ist.

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