Download PDF by Radu Laza, Matthias Schütt, Noriko Yui: Calabi-Yau Varieties: Arithmetic, Geometry and Physics:

Algebraic Geometry

By Radu Laza, Matthias Schütt, Noriko Yui

This quantity provides a full of life creation to the quickly constructing and significant study parts surrounding Calabi–Yau kinds and string thought. With its insurance of a number of the views of a large region of themes reminiscent of Hodge idea, Gross–Siebert application, moduli difficulties, toric method, and mathematics points, the publication provides a finished evaluation of the present streams of mathematical learn within the area.

The contributions during this ebook are according to lectures that came about in the course of workshops with the next thematic titles: “Modular varieties round String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics round reflect Symmetry,” “Hodge conception in String Theory.” The booklet is perfect for graduate scholars and researchers studying approximately Calabi–Yau kinds in addition to physics scholars and string theorists who desire to research the maths in the back of those varieties.

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Additional info for Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses

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In: Bourbaki Seminar, Vol. 1982/83. Volume 105 of Astérisque, pp. 251–278. Société mathématique de France, Paris (1983) The Geometry and Moduli of K3 Surfaces 41 14. : Mirror symmetry for lattice polarised K3 surfaces. J. Math. Sci. 81(3), 2599– 2630 (1996) 15. : Shimura curve computations via K3 surfaces of Néron-Severi rank at least 19. In: Algorithmic Number Theory. Volume 5011 of Lecture Notes in Computer Science, pp. 196–211. Springer, Berlin (2008) 16. : K3 surfaces and equations for Hilbert modular surfaces.

The key tools that we use are Shioda maps and information about the middle cohomology of Fermat varieties. We will use a Shioda map to relate each surface of BHK type birationally to a quotient of a higher degree Fermat hypersurface in projective space by a finite group H. , the Lefschetz number. L. Kelly Take BHK mirrors surfaces ZA;G and ZAT ;GT as above over a field of characteristic p or characteristic 0.

S; / be an elliptically fibred surface with a chosen zero section O. S; /. S; / corresponds directly to the pointwise addition in each smooth fibre. S; / does not depend upon the choice of section O, hence our notation for the Mordell-Weil group does not make reference to it. S; /, its Mordell-Weil group, and its singular fibres. S; /, which we will use as the identity element. p/ as a sum of irreducible components C0 ; : : : ; Cn as before, labelled so that C0 is the component which intersects the zero section O, then let Rp be 28 A.

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