By Radu Laza, Matthias Schütt, Noriko Yui

This quantity provides a full of life creation to the speedily constructing and monstrous study components surrounding Calabi–Yau types and string conception. With its insurance of many of the views of a large sector of themes comparable to Hodge concept, Gross–Siebert software, moduli difficulties, toric procedure, and mathematics facets, the ebook supplies a complete assessment of the present streams of mathematical learn within the area.

The contributions during this e-book are in line with lectures that happened in the course of workshops with the next thematic titles: “Modular varieties round String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics round replicate Symmetry,” “Hodge concept in String Theory.” The publication is perfect for graduate scholars and researchers studying approximately Calabi–Yau types in addition to physics scholars and string theorists who desire to examine the math in the back of those varieties.

**Read Online or Download Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses PDF**

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

**Example text**

Fano threefolds and K3 surfaces. In: The Fano Conference, pp. 175–184. Univ. Torino, Turin (2004) 9. : Picard lattices of families of K3 surfaces. Commun. Algebra 30(1), 61–82 (2002) 10. : Modular invariants for lattice polarized K3 surfaces. Michigan Math. J. 55(2), 355–393 (2007) 11. : Normal forms, K3 surface moduli and modular parametrizations. In: Groups and Symmetries. Volume 47 of CRM Proceedings and Lecture Notes, pp. 81–98. American Mathematical Society, Providence (2009) 12. : Enriques Surfaces.

169, 239–242 (1967) 36. : Degenerations of K3 surfaces and Enriques surfaces. Math. USSR Izv. 11(5), 957–989 (1977) 37. : On modifications of degenerations of surfaces with Ä D 0. Math. USSR Izv. 17(2), 339–342 (1981) 38. : On minimally elliptic singularities. Am. J. Math. 99(6), 1257–1295 (1977) 42 A. Harder and A. Thompson 39. : The KSBA compactification for the moduli space of degree two K3 pairs (2012, preprint). 3144 40. : Characterization of Moishezon manifolds. In: Holomorphic Morse Inequalities and Bergman Kernels.

Then any fibre E of is either: The Geometry and Moduli of K3 Surfaces 23 1. Irreducible, in which case E is either a smooth elliptic curve, or a nodal or cuspidal rational curve; or 2. Reducible, in which case E is a configuration of smooth rational curves Ci with hŒCi ; ŒCi i D 2. In this case E is either a pair of rational curves that are tangent at a point, three rational curves meeting at a single point, or a configuration of rational curves meeting transversely with dual intersection graph of extended ADE type.