Toric degenerations of Fano threefolds giving weak Landau–Ginzburg models
TLDR
In this article, it was shown that every Picard rank one smooth Fano threefold has a weak Landau-Ginzburg model coming from a toric degeneration, which can be compactified to K3 surfaces with Picard lattice of rank 19.About:
This article is published in Journal of Algebra.The article was published on 2013-01-15 and is currently open access. It has received 50 citations till now. The article focuses on the topics: Fano variety & Fano plane.read more
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Weak Landau-Ginzburg models for smooth Fano threefolds
TL;DR: In this article, it was shown that Landau-Ginzburg models for all 17 smooth Fano threefolds with Picard rank 1 can be represented as Laurent polynomials in 3 variables exhibiting them case by case.
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Hori-Vafa mirror models for complete intersections in weighted projective spaces and weak Landau-Ginzburg models
TL;DR: In this article, it was shown that Hori-Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials, and they were shown to admit a Laplacian interpretation as well.
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Seshadri constants via toric degenerations
TL;DR: In this article, the Seshadri constants on hypersurfaces in projective spaces and Fano 3-folds with Picard number one were estimated at any point on toric varieties.
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Four-dimensional Fano toric complete intersections.
TL;DR: In this paper, the authors find at least 527 new four-dimensional Fano manifolds, each of which is a complete intersection in a smooth toric Fano manifold, and each of these manifolds can be represented as
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On Hodge numbers of complete intersections and Landau--Ginzburg models
TL;DR: In this paper, it was shown that the Hodge number of the central fiber of a Calabi-Yau compactification of Givental's Landau-Ginzburg model is less by one than the number of irreducible components.
References
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Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Journal Article
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.
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Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.
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Classification of Fano 3-folds with B2≥2
TL;DR: The classification of Fano 3-folds with B2≥2 is studied in this paper, where the second Betti number of a 3-fold is not greater than 10.