Main Algebraic Geometry: Notes on a Course (Graduate Studies in Mathematics, 222)
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Algebraic Geometry: Notes on a Course (Graduate Studies in Mathematics, 222)

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This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. $mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem.
Request Code : ZLIBIO4355833
Categories:
Year:
2022
Publisher:
Amer Mathematical Society
Language:
English
Pages:
318
ISBN 10:
1470468484
ISBN 13:
9781470468484
ISBN:
1470468484,9781470468484

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