A class of twisted special Lagrangian submanifolds in T＊R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed.
We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a s...We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a square matrix Q of polynomial entries satisfying Q^(2)=W·Id.We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances.Our main example is the Lagrangian submanifold RP^(2)⊂CP^(2)and its mirror ungraded matrix factorization,which we construct and study.In particular,we prove a version of Homological Mirror Symmetry in this setting.展开更多
文摘A class of twisted special Lagrangian submanifolds in T＊R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(Grant No.2020R1A5A1016126)。
文摘We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a square matrix Q of polynomial entries satisfying Q^(2)=W·Id.We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances.Our main example is the Lagrangian submanifold RP^(2)⊂CP^(2)and its mirror ungraded matrix factorization,which we construct and study.In particular,we prove a version of Homological Mirror Symmetry in this setting.
基金This works is supported by the National Natural Science Foundation of China(No.10261004).The first author was supported by Visiting Scholar Foundation of Key Lab.in University and Natural Science Foundation of Inner Mongolia(20010901-06)
