Related papers: Mirror Symmetry Constructions
In this paper, we establish equivariant mirror symmetry for the weighted projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017].…
Mirror symmetry, a phenomenon in superstring theory, has recently been used to give tentative calculations of several numbers in algebraic geometry. In this paper, the numbers of lines and conics on various hypersurfaces which satisfy…
We study a mirror interpretation of the relation between the exact partition functions of N=(2,2) gauged linear sigma-models (GLSM) on the 2d sphere and Kahler potentials on the moduli spaces of the CY manifolds proposed by Jockers et al.…
This paper establishes BCOV-type genus one mirror symmetry for the intersections of two cubics in $\mathbb{P}^5$. The proof applies previous constructions of the mirror family by the second author and computations of genus one Gromov-Witten…
Associativity of the quantum product ensures flatness of the Dubrovin connection and is the basis for Hodge-theoretic mirror symmetry of Calabi-Yau threefolds. We use ring and module structure on cohomology pertaining to a Lagrangian…
We consider the CY orbifolds connected with the products of N = (2, 2) supersymmetric minimal models. We use the spectral flow construction of states, as well as its mirror one, to explicitly show that these CY orbifolds are canonically…
We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge…
Localization methods have produced explicit expressions for the sphere partition functions of (2,2) superconformal field theories. The mirror symmetry conjecture predicts an IR duality between pairs of Abelian gauged linear sigma models, a…
In the algebraic setting, cluster varieties were reformulated by Gross-Hacking-Keel as log Calabi-Yau varieties admitting a toric model. Building on work of Shende-Treumann-Williams-Zaslow in dimension 2, we describe the mirror to the GHK…
For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has proposed a possible mirror partner (which is also a family of Calabi-Yau hypersurfaces). We explain a natural construction of the isomorphism between certain Hodge…
We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories…
We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential…
The construction of mirror symmetry in the heterotic string is reviewed in the context of Calabi-Yau and Landau-Ginzburg compactifications. This framework has the virtue of providing a large subspace of the configuration space of the…
Recently two groups have listed all sets of weights (k_1,...,k_5) such that the weighted projective space P_4^{(k_1,...,k_5)} admits a transverse Calabi-Yau hypersurface. It was noticed that the corresponding Calabi-Yau manifolds do not…
For certain quasismooth Calabi-Yau hypersurfaces in weighted projective space, the Berglund-H\"{u}bsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mirror. We prove that the minimal log discrepancy of the…
After the appearance of my preprint [T3] (Special Lagrangian geometry and slightly deformed algebraic geometry (spLag and sdAG), Warwick preprint 22/1998, alg-geom/9806006, 54 pp.). I received an e-mail from Cumrun Vafa, who recognized that…
We prove a derived analogue to the results of Borisov, Clarke, Kelly, and Shoemaker on the birationality of Berglund-Hubsch-Krawitz mirrors. Heavily bootstrapping off work of Seidel and Sheridan, we obtain Homological Mirror Symmetry for…
Calabi--Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky--Cecotti--Ooguri--Vafa (BCOV), it is expected that genus 1 curve counting on a Calabi--Yau…
Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$…
We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev-Nill…