TY  - BOOK
AU  - Artin,Michael
TI  - Algebraic geometry: notes on a course
T2  - Graduate studies in mathematics,
SN  - 9781470471118
U1  - 512.7 
PY  - 2022///
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Geometry, Algebraic
KW  - Algebraic geometry -- Instructional exposition (textbooks, tutorial papers, etc.)
N1  - Includes bibliographical references (pages 313-314) and index; Undergraduate and graduate students interested in learning and teaching algebraic geometry
N2  - 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. 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 P3,and double planes, and it ends with applications of the Riemann-Roch Theorem
UR  - https://www.ams.org/bookstore/pspdf/gsm-222-toc.pdf?_gl=1*1lhyl5f*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMxNzEzMi4wLjAuMA..
UR  - https://www.ams.org/bookstore/pspdf/gsm-222-index.pdf?_gl=1*r4v97c*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMxNzEzMy4wLjAuMA..
UR  - https://www.goodreads.com/book/show/61722980-algebraic-geometry?from_search=true&from_srp=true&qid=Rb9DSiI9ZC&rank=1#CommunityReviews
ER  -