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대수기하학에서 토렐리 정리(Torelli定理, 영어: Torelli theorem)는 리만 곡면이 그 야코비 다양체에 의하여 결정된다는 정리다. 즉, 리만 곡면의 모듈라이 공간에서 야코비 다양체로의 사상은 단사 함수이다. K3 곡면과 칼라비-야우 다양체의 경우에도 유사한 정리가 존재한다.
, In mathematics, the Torelli theorem, named … In mathematics, the Torelli theorem, named after Ruggiero Torelli, is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) C is determined by its Jacobian variety J(C), when the latter is given in the form of a principally polarized abelian variety. In other words, the complex torus J(C), with certain 'markings', is enough to recover C. The same statement holds over any algebraically closed field. From more precise information on the constructed isomorphism of the curves it follows that if the canonically principally polarized Jacobian varieties of curves of genus are k-isomorphic for k any perfect field, so are the curves. This result has had many important extensions. It can be recast to read that a certain natural morphism, the period mapping, from the moduli space of curves of a fixed genus, to a moduli space of abelian varieties, is injective (on geometric points). Generalizations are in two directions. Firstly, to geometric questions about that morphism, for example the . Secondly, to other period mappings. A case that has been investigated deeply is for K3 surfaces (by , Ilya Pyatetskii-Shapiro, Igor Shafarevich and Fedor Bogomolov) and hyperkähler manifolds (by Misha Verbitsky, and Daniel Huybrechts).y Misha Verbitsky, and Daniel Huybrechts).
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In mathematics, the Torelli theorem, named … In mathematics, the Torelli theorem, named after Ruggiero Torelli, is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) C is determined by its Jacobian variety J(C), when the latter is given in the form of a principally polarized abelian variety. In other words, the complex torus J(C), with certain 'markings', is enough to recover C. The same statement holds over any algebraically closed field. From more precise information on the constructed isomorphism of the curves it follows that if the canonically principally polarized Jacobian varieties of curves of genus are k-isomorphic for k any perfect field, so are the curves.or k any perfect field, so are the curves.
, 대수기하학에서 토렐리 정리(Torelli定理, 영어: Torelli theorem)는 리만 곡면이 그 야코비 다양체에 의하여 결정된다는 정리다. 즉, 리만 곡면의 모듈라이 공간에서 야코비 다양체로의 사상은 단사 함수이다. K3 곡면과 칼라비-야우 다양체의 경우에도 유사한 정리가 존재한다.
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토렐리 정리
, Torelli theorem
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