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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.
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참고문헌 (15)
참고문헌 신청
M. Abouzaid / 2010 / Homological mirror symmetry for the 4-torus / Duke Math. J 152(3):373~440
P. S. Aspinwall / 2007 / Landau-Ginzburg to Calabi-Yau dictionary for D-branes / J. Math. Phys 48(8):18
D. Auroux / 2014 / A beginner's introduction to Fukaya categories, in Contact and symplectic topology / Bolyai Soc. Math. Stud. 26:85~136
A. Caldararu / 2013 / Curved A1 algebras and Landau-Ginzburg models / New York J. Math 19:305~342
C. -H. Cho / 2017 / Localized mirror functor for Lagrangian immer-sions, and homological mirror symmetry for P1a;b;c / J. Dierential Geom 106(1):45~126
P. S. Aspinwall / 2007 / Landau-Ginzburg to Calabi-Yau dictionary for D-branes / J. Math. Phys 48(8):18
D. Auroux / 2014 / A beginner's introduction to Fukaya categories, in Contact and symplectic topology / Bolyai Soc. Math. Stud. 26:85~136
A. Caldararu / 2013 / Curved A1 algebras and Landau-Ginzburg models / New York J. Math 19:305~342
C. -H. Cho / 2017 / Localized mirror functor for Lagrangian immer-sions, and homological mirror symmetry for P1a;b;c / J. Dierential Geom 106(1):45~126
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