By V. A. Vassiliev

ISBN-10: 0821829483

ISBN-13: 9780821829486

Many very important features of mathematical physics are outlined as integrals looking on parameters. The Picard-Lefschetz conception experiences how analytic and qualitative houses of such integrals (regularity, algebraicity, ramification, singular issues, etc.) depend upon the monodromy of corresponding integration cycles. during this publication, V. A. Vassiliev provides numerous models of the Picard-Lefschetz concept, together with the classical neighborhood monodromy conception of singularities and entire intersections, Pham's generalized Picard-Lefschetz formulation, stratified Picard-Lefschetz thought, and in addition twisted types of most of these theories with functions to integrals of multivalued varieties. the writer additionally indicates how those models of the Picard-Lefschetz idea are utilized in learning various difficulties coming up in lots of parts of arithmetic and mathematical physics. specifically, he discusses the next periods of services: quantity features coming up within the Archimedes-Newton challenge of integrable our bodies; Newton-Coulomb potentials; basic options of hyperbolic partial differential equations; multidimensional hypergeometric services generalizing the classical Gauss hypergeometric crucial. The ebook is aimed at a vast viewers of graduate scholars, learn mathematicians and mathematical physicists attracted to algebraic geometry, advanced research, singularity concept, asymptotic equipment, capability thought, and hyperbolic operators.

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**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.

### Applied Picard--Lefschetz Theory by V. A. Vassiliev

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