Song He picked up the short test again and scrutinized it with a furrowed brow. But after reading the question several times, he was still utterly lost.
Dewitt smiled kindly. "Even if O is smooth everywhere on L², that doesn't mean it's smooth on the plane at infinity."
"Oh, that!" Song He suddenly understood. "You just need to resolve the singularity at the singular point."
This time, Dewitt was the one left stunned. A flash of astonishment crossed his eyes, and his expression seemed to say, There's such a method?
Katerina was curious. "What do you mean?"
"Blow it up repeatedly until you get a nonsingular curve," Song He explained. "If all the higher-order derivatives of O are zero, resolving the singularity will be somewhat more complicated. Fortunately, this problem only asks for the compactification of an algebraic curve under two-dimensional conditions, so we can directly apply the Riemann existence theorem—in other words, construct a compact Riemann surface."
Katerina's mouth formed a small O. "I sort of understand, but... your approach is rather unconventional, isn't it?"
"It's definitely not the standard solution. It's practically a crooked trick, which is why I didn't mention it. Your method is quite good—steady and reliable, with no risk of mistakes," Song He admitted.
Katerina and Galois turned their heads together to observe Dewitt's reaction.
Dewitt didn't comment, merely giving an ambiguous chuckle. "I've more or less memorized the first question. How about we look at the second?"
This time, Galois beat them to the answer. "It can be solved in three steps!"
"Exactly!" Katerina nodded.
Song He remained silent, quietly waiting for the dishes to arrive.
The same scene continued to repeat itself over the next few questions.
Galois and Katerina were extremely enthusiastic in their solutions. Their rapid-fire exchanges were comparable to two