Algebraic Geometry: Notes on a Course (Graduate Studies in Mathematics) - Softcover

Artin, Michael

Softcover

ISBN 10: 1470471116 ISBN 13: 9781470471118

Verlag: American Mathematical Society, 2022

Inhaltsangabe

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 construcibility. $\mathcal{O}$-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.

Über diesen Titel

Über die Autorin bzw. den Autor

Michael Artin, Massachusetts Institute of Technology, Cambridge, MA.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2022
• Sprache: Englisch
• ISBN 10: 1470471116
• ISBN 13: 9781470471118
• Einband: Tapa blanda
• Anzahl der Seiten: 322
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar