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Graphics industry --- Music --- History of Antwerp --- Algemeen-Vlaamsche Muziekuitgave de Ring [Berchem]

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Richard Wagner's opera Das Rheingold is a milestone in the composer's output and in the history of music in general. It marked Wagner's return to operatic composition after a hiatus of five years, and signified his definitive break with earlier operatic conventions. It also represents a reconsideration of the whole question of dramatic-musical form, and the role of tonality in articulating this form. Warren Darcy traces here the genesis of Das Rheingold through the various textual and musical sketches and drafts to the full score, and also develops a theoretical framework within which the opera may be meaningfully analysed. Using Wagner's manuscripts as a point of departure, Darcy discusses the formal, harmonic, and linear structure of the work. In so doing, he challenges a number of contemporary views about the opera, including those of Curt von Westernhagen and Carl Dahlhaus.

Wagner, Richard --- Wagner, Richard, --- Operas --- Opéras --- Operas. --- Analysis, appreciation. --- Stories, plots, etc. --- Analyse et appréciation. --- Ring des Nibelungen (Wagner, Richard)

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Art styles --- Art --- Drawing --- Painting --- collages [visual works] --- relief [sculpture techniques] --- drawing [image-making] --- painting [image-making] --- watercolors [paintings] --- India ink [ink] --- Futurist --- Constructivist --- Cubist --- Ring, Thomas --- anno 1900-1909 --- anno 1910-1919 --- anno 1920-1929 --- anno 1930-1939

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Asymmetric synthesis --- Catalysis --- Catalyse --- Asymmetric synthesis. --- Catalysis. --- 547.057 --- 544.47 --- #WSCH:LOSH --- Activation (Chemistry) --- Chemistry, Physical and theoretical --- Surface chemistry --- Asymmetric induction --- Induction, Asymmetric --- Synthesis, Asymmetric --- Asymmetry (Chemistry) --- Organic compounds --- Organic chemistry--?.057 --- Catalysis. Catalytic reactions --- Synthesis --- 547.057 Organic chemistry--?.057 --- CATALYSIS --- ASYMMETRIC SYNTHESIS --- HYDROGENATION --- ISOMERIZATION --- OXIDATION --- CARBONYLATION --- HYDROSILYLATION --- BOND --- RING CLOSURE --- CARBON-CARBON

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Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories.The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.

Algebraic geometry --- Differential geometry. Global analysis --- 512.7 --- Algebraic geometry. Commutative rings and algebras --- Toric varieties. --- 512.7 Algebraic geometry. Commutative rings and algebras --- Toric varieties --- Embeddings, Torus --- Torus embeddings --- Varieties, Toric --- Algebraic varieties --- Addition. --- Affine plane. --- Affine space. --- Affine variety. --- Alexander Grothendieck. --- Alexander duality. --- Algebraic curve. --- Algebraic group. --- Atiyah–Singer index theorem. --- Automorphism. --- Betti number. --- Big O notation. --- Characteristic class. --- Chern class. --- Chow group. --- Codimension. --- Cohomology. --- Combinatorics. --- Commutative property. --- Complete intersection. --- Convex polytope. --- Convex set. --- Coprime integers. --- Cotangent space. --- Dedekind sum. --- Dimension (vector space). --- Dimension. --- Direct proof. --- Discrete valuation ring. --- Discrete valuation. --- Disjoint union. --- Divisor (algebraic geometry). --- Divisor. --- Dual basis. --- Dual space. --- Equation. --- Equivalence class. --- Equivariant K-theory. --- Euler characteristic. --- Exact sequence. --- Explicit formula. --- Facet (geometry). --- Fundamental group. --- Graded ring. --- Grassmannian. --- H-vector. --- Hirzebruch surface. --- Hodge theory. --- Homogeneous coordinates. --- Homomorphism. --- Hypersurface. --- Intersection theory. --- Invertible matrix. --- Invertible sheaf. --- Isoperimetric inequality. --- Lattice (group). --- Leray spectral sequence. --- Limit point. --- Line bundle. --- Line segment. --- Linear subspace. --- Local ring. --- Mathematical induction. --- Mixed volume. --- Moduli space. --- Moment map. --- Monotonic function. --- Natural number. --- Newton polygon. --- Open set. --- Picard group. --- Pick's theorem. --- Polytope. --- Projective space. --- Quadric. --- Quotient space (topology). --- Regular sequence. --- Relative interior. --- Resolution of singularities. --- Restriction (mathematics). --- Resultant. --- Riemann–Roch theorem. --- Serre duality. --- Sign (mathematics). --- Simplex. --- Simplicial complex. --- Simultaneous equations. --- Spectral sequence. --- Subgroup. --- Subset. --- Summation. --- Surjective function. --- Tangent bundle. --- Theorem. --- Topology. --- Toric variety. --- Unit disk. --- Vector space. --- Weil conjecture. --- Zariski topology.