Mirror symmetry and T-duality in the complement of an anticanonical divisor

By D. Auroux. 2007

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We study the geometry of complexified moduli spaces of special Lagrangian submanifolds in the complement of an anticanonical divisor in a compact Kahler manifold. In particular, we explore the connections between T-duality and mirror symmetry in concrete examples, and show how quantum corrections arise in this context.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8db5f1fbec3c7cdf62ec0bb35f8149b0c00f1999

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Citations in the corpus

Homological mirror symmetry for the genus two curve (2008, background): “A G ] 7 S ep 2 00 9 Homological mirror symmetry for the genus two curve Paul Seidel v5; September 7, 2009”
The wall-crossing formula and Lagrangian mutations (2017, methodology): “The statement from the last item is the wall-crossing formula which has been predicted by Auroux [3], and in a slightly different context by Kontsevich and Soibelman [23].”
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, background): “The gluing maps for the mirrors of nearby chambers are given by wall-crossing formulae, with instanton corrections accounting for the disc bubbling phenomena that occur as a Lagrangian submanifold is isotoped across a wall of potentially obstructed Lagrangians (see [3] for an informal discussion, an”
Geometry of canonical bases and mirror symmetry (2013, methodology): “s the cycle class [Dc] ∈H2(ML,Z(1)) of the divisor Dc. ii) The Landau-Ginzburg potential Wc should be obtained by counting the holomorphic discs touching the divisor Dc, as was demonstrated by Auroux [Au1] in examples. iii) In the cluster variety set up the correspondence is much more precise, see S”
Symplectic Cohomology and q-Intersection Numbers (2010, background): “The dilation condition corresponds to asking for our vector field to contract the holomorphic volume form on X , at least in those cases where the mirror construction is based on such a form (as one can see from [7] for instance, mirrors of open manifolds can also be constructed using volume forms w”
Infinitely many exotic monotone Lagrangian tori in ℂℙ2 (2014, background): “7 of [2] or equation (2-2) in [15]), we can identify the boundary Maslov-2 convex hull of L with the Newton polytope of the superpotential of L.”
Cluster varieties from Legendrian knots (2015, background): “nce at one instant of a single double point, the families of objects deﬁned by rank one local systems before and after the critical moment are algebraic tori related by a cluster transformation (c.f. [Aur] or [Sei2, Lec. 11], for example). Here we will give an account of the existence of cluster str”
Floer cohomology and pencils of quadrics (2010, background): “P. Seidel and I. Smith.”
The monotone wrapped Fukaya category and the open-closed string map (2012, methodology): “For L = Li = Lj one can use a Morse-Bott model using C∗(L) = CF (L,L) as carried out by Auroux [12].”
Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, background): “More precisely, there is a full subcategory of F(Ē) whose objects are exact Lagrangian submanifolds in E (this appears for instance in [7]), and one can conjecture that this should be isomorphic to a full subcategory of the Landau-Ginzburg category.”
Punctured holomorphic curves and Lagrangian embeddings (2014, background): “(c) Carrying over arguments from [14] to the CP(2) case, it is shown in [4] that each of the relative homology classes of Maslov number 2 listed in Lemma A.”