By Joe Harris
A consultant to a wealthy and engaging topic: algebraic curves and the way they range in s. offering a vast yet compact evaluation of the sphere, this e-book is offered to readers with a modest historical past in algebraic geometry. It develops many options, together with Hilbert schemes, deformation conception, strong aid, intersection concept, and geometric invariant conception, with the focal point on examples and functions coming up within the learn of moduli of curves. From such foundations, the e-book is going directly to express how moduli areas of curves are built, illustrates commonplace functions with the proofs of the Brill-Noether and Gieseker-Petri theorems through restrict linear sequence, and surveys an important effects approximately their geometry starting from irreducibility and entire subvarieties to considerable divisors and Kodaira size. With over a hundred and eighty routines and 70 figures, the ebook additionally offers a concise creation to the most effects and open difficulties approximately vital themes which aren't lined intimately.
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