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곡선의 정의란 무엇인가?

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Lecturer 김영훈
Dept. 서울대학교
date Dec 02, 2010

곡선은 방정식, 매개화된 곡선의 동치류, 모듈 등의 다양한 관점에서 정의될 수 있다. 미끈한 곡선의 경우는 모든 정의들이 본질적으로 동등하지만 이들의 극한을 취하면 관점에 따라 완전히 다른 답들이 얻어진다. 따라서 미끈한 곡선들의 집합은 관점에 따라 다양한 긴밀화를 가진다. 이러한 긴밀화를 통해 어떻게 곡선을 세는 불변량(그로모프-위튼, 도날슨-토마스, … )들이 얻어지는지 살펴보고 이들을 어떻게 계산할지 그리고 어떻게 비교할지 알아본다.

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