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Comparison of mirror functors of elliptic curves via LG/CY correspondence

Sangwook Lee
대한수학회 (The Korean Mathematical Society)|2020.09|대한수학회지 (Journal of the KMS)|제57권 제5호|pp. 1135-1165|DOI 10.4134/JKMS.j190589

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참고문헌

키워드

LG/CY correspondencehomological mirror symmetry
주제분류수학

초록

Polishchuk-Zaslow explained the homological mirror symmetry between Fukaya category of symplectic torus and the derived category of coherent sheaves of elliptic curves via Lagrangian torus fibration. Recently, Cho-Hong-Lau found another proof of homological mirror symmetry using localized mirror functor, whose target category is given by graded matrix factorizations. We find an explicit relation between these two approaches.

Abstract

Polishchuk-Zaslow explained the homological mirror symmetry between Fukaya category of symplectic torus and the derived category of coherent sheaves of elliptic curves via Lagrangian torus fibration. Recently, Cho-Hong-Lau found another proof of homological mirror symmetry using localized mirror functor, whose target category is given by graded matrix factorizations. We find an explicit relation between these two approaches.

참고문헌 (15)

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  11. D. Orlov, "Derived categories of coherent sheaves and triangulated categories of sin-gularities, in Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II", Progr. Math, 270, pp.503~531 (2009), Birkhauser Boston, Inc[DOI]
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