Moduli of Weighted Hyperplane Arrangements electronic resource by Valery Alexeev ; edited by Gilberto Bini, Martí Lahoz, Emanuele Macrí, Paolo Stellari.
Material type: TextSeries: Advanced Courses in Mathematics - CRM BarcelonaPublication details: Basel : Springer Basel : Imprint: Birkhäuser, 2015Description: VII, 104 p. 50 illus., 16 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783034809153Subject(s): mathematics | Algebraic Geometry | Convex geometry | Discrete geometry | Mathematics | Algebraic Geometry | Convex and Discrete GeometryDDC classification: 516.35 LOC classification: QA564-609Online resources: Click here to access onlinePreface -- Introduction -- Stable pairs and their moduli -- Stable toric varieties -- Matroids -- Matroid polytopes and tilings -- Weighted stable hyperplane arrangements -- Abelian Galois covers -- Bibliography.
This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory – to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements.
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