کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1894664 1533740 2015 31 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Landau–Ginzburg systems, quivers and monodromy
ترجمه فارسی عنوان
در سیستم های لندوآ گینزبورگ، دودکش ها و یکنواختی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی

Let XX be a toric Fano manifold and denote by Crit(fX)⊂(C∗)nCrit(fX)⊂(C∗)n the solution scheme of the corresponding Landau–Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map L:Crit(fX)→Pic(X)L:Crit(fX)→Pic(X) such that EL(X):=L(Crit(fX))⊂Pic(X)EL(X):=L(Crit(fX))⊂Pic(X) is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map M:π1(L(X)∖RX,fX)→Aut(Crit(fX))M:π1(L(X)∖RX,fX)→Aut(Crit(fX)) where L(X)L(X) is the space of all Laurent polynomials whose Newton polytope is equal to the Newton polytope of fXfX, the Landau–Ginzburg potential of XX, and RX⊂L(X)RX⊂L(X) is the space of all elements whose corresponding solution scheme is reduced. We show that monodromies of Crit(fX)Crit(fX) admit non-trivial relations to quiver representations of the exceptional collection EL(X)EL(X). We refer to this property as the MM-aligned property of the maps L:Crit(fX)→Pic(X)L:Crit(fX)→Pic(X). We discuss possible applications of the existence of such MM-aligned exceptional maps to various aspects of mirror symmetry of toric Fano manifolds.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 98, December 2015, Pages 504–534
نویسندگان
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