New PDF release: Calabi-Yau Varieties: Arithmetic, Geometry and Physics:

By Radu Laza, Matthias Schütt, Noriko Yui

ISBN-10: 1493928295

ISBN-13: 9781493928293

ISBN-10: 1493928309

ISBN-13: 9781493928309

This quantity offers a full of life creation to the quickly constructing and huge examine components surrounding Calabi–Yau kinds and string conception. With its insurance of many of the views of a large sector of themes corresponding to Hodge idea, Gross–Siebert software, moduli difficulties, toric technique, and mathematics points, the e-book supplies a accomplished evaluate of the present streams of mathematical study within the area.

The contributions during this publication are in line with lectures that came about in the course of workshops with the next thematic titles: “Modular kinds round String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics round replicate Symmetry,” “Hodge thought 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 at the back of those varieties.

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

Sample text

Det A ¤ 0. q0 ; : : : ; qn /. Any surface XA constructed this way is called a weighted Delsarte hypersurface. In particular, if n D 3 we say that XA is a weighted Delsarte surface. It is our goal to compute the Picard ranks of certain symplectic quotients of (quasi-smooth) weighted Delsarte surfaces that are K3 surfaces. In order to solve this problem, we introduce a mirror symmetry viewpoint. In 1990, the idea of a duality of moduli spaces via a mirror was brought to light by Greene and Plesser in [11].

In: Complex Algebraic Geometry (Park City, UT, 1993). Volume 3 of IAS/Park City Mathematics Series, pp. 3–159. American Mathematical Society, Providence (1997) 57. : Lattice polarized toric K3 surfaces (2004, preprint). arXiv:hep-th/0409290 58. : Calabi-Yau-Hyperflächen in Torischen Varietäten, Faserungen und Dualitäten. PhD thesis, Rheinische Friedrich-Wilhelms-Universität Bonn (2005) 59. : On the compactification of moduli spaces for algebraic K3 surfaces. Mem. Am. Math. Soc. 70(374) (1987) 60.

73(1), 139–150 (1983) 66. : Finiteness results for algebraic K3 surfaces. Math. Z. 189(4), 507–513 (1985) 67. : Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular Functions of One Variable IV. Volume 476 of Lecture Notes in Mathematics, pp. 33–52. Springer, Berlin/Heidelberg (1975) 68. : Kuga-Satake varieties and the Hodge conjecture. In: The Arithmetic and Geometry of Algebraic Cycles (Banff, AB, 1998). Volume 548 of Nato Science Series C: Mathematical and Physical Sciences, pp.

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Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses by Radu Laza, Matthias Schütt, Noriko Yui

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