• 제목/요약/키워드: derived category of coherent sheaves

검색결과 4건 처리시간 0.017초

EQUIVARIANT MATRIX FACTORIZATIONS AND HAMILTONIAN REDUCTION

  • Arkhipov, Sergey;Kanstrup, Tina
    • 대한수학회보
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    • 제54권5호
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    • pp.1803-1825
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    • 2017
  • Let X be a smooth scheme with an action of an algebraic group G. We establish an equivalence of two categories related to the corresponding moment map ${\mu}:T^{\ast}X{\rightarrow}g^{\ast}$ - the derived category of G-equivariant coherent sheaves on the derived fiber ${\mu}^{-1}(0)$ and the derived category of G-equivariant matrix factorizations on $T^{\ast}X{\times}g$ with potential given by ${\mu}$.

COMPARISON OF MIRROR FUNCTORS OF ELLIPTIC CURVES VIA LG/CY CORRESPONDENCE

  • Lee, Sangwook
    • 대한수학회지
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    • 제57권5호
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    • pp.1135-1165
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    • 2020
  • 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.

WEIGHTED PROJECTIVE LINES WITH WEIGHT PERMUTATION

  • Han, Lina;Wang, Xintian
    • 대한수학회지
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    • 제58권1호
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    • pp.219-236
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    • 2021
  • Let �� be a weighted projective line defined over the algebraic closure $k={\bar{\mathbb{F}}}_q$ of the finite field ��q and σ be a weight permutation of ��. By folding the category coh-�� of coherent sheaves on �� in terms of the Frobenius twist functor induced by σ, we obtain an ��q-category, denoted by coh-(��, σ; q). We then prove that coh-(��, σ; q) is derived equivalent to the valued canonical algebra associated with (��, σ).

CLASSIFICATION OF FULL EXCEPTIONAL COLLECTIONS OF LINE BUNDLES ON THREE BLOW-UPS OF ℙ3

  • Liu, Wanmin;Yang, Song;Yu, Xun
    • 대한수학회지
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    • 제56권2호
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    • pp.387-419
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    • 2019
  • A fullness conjecture of Kuznetsov says that if a smooth projective variety X admits a full exceptional collection of line bundles of length l, then any exceptional collection of line bundles of length l is full. In this paper, we show that this conjecture holds for X as the blow-up of ${\mathbb{P}}^3$ at a point, a line, or a twisted cubic curve, i.e., any exceptional collection of line bundles of length 6 on X is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such X.