Titlebook: Calabi-Yau Varieties: Arithmetic, Geometry and Physics; Lecture Notes on Con Radu Laza,Matthias Schütt,Noriko Yui Book 2015 Springer Scienc

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The Geometry and Moduli of K3 Surfacesexplicit examples, including a large class of lattice polarizations coming from elliptic fibrations. Finally, we conclude by discussing the ample and K?hler cones of K3 surfaces, and give some of their applications.

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Picard Ranks of K3 Surfaces of BHK Typegree to that of the K3 surfaces in question. The end result shows that the Picard ranks of a K3 surface of BHK-type and its BHK mirror are intrinsically intertwined. We end with an example of BHK mirror surfaces that, over certain fields, are supersingular.

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Picard Ranks of K3 Surfaces of BHK Typeth in characteristic zero and in positive characteristic. These K3 surfaces are those that are certain orbifold quotients of weighted Delsarte surfaces. The proof is an updated classical approach of Shioda using rational maps to relate the transcendental lattice of a Fermat hypersurface of higher de

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Reflexive Polytopes and Lattice-Polarized K3 Surfacesof mirror symmetry for K3 surfaces which relies on a sublattice of the Picard lattice. We then show how to combine information about the Picard group of a toric ambient space with data about automorphisms of the toric variety to identify families of K3 surfaces with high Picard rank.

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Introduction to Gromov–Witten Theoryese notes are based on a talk given at the Fields Institute during a week-long conference aimed at introducing graduate students to the subject which took place during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics.

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Introduction to Donaldson–Thomas and Stable Pair InvariantsStable Pair invariants. We elaborate on some aspects of the expostion in the survey paper by Pandharipande-Thomas. Our emphasis is on one hand on examples that illustrate the properties of the relevant moduli spaces, on the other hand on discussing some of the highlights of the theory.