Algebraic Geometry – Mathematical Association of America

Featured Resources

From wandering to wayfinding: Moving Beyond Shiny Object Syndrome

By Lew Ludwig "The deep breath before the plunge" - a sentiment Gandalf shares with Pippin in the Return of the King. This phrase often runs through my mind as the last days of summer break wind down and the new school year is about to begin. To be clear, I do not see the new...

Complement (bottom-up) learning with top-down activities to develop mathematical thinking ability

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social Sometime in the early 2000s, my primary care physician offered me the option of no longer having an annual health checkup in person. Rather, I could just call into my nearest walk-in testing lab and have a blood draw, followed up a few days later by a quick video-chat. (They also wanted...

Exploring Discrete Geometry

Discrete geometry is field that lies on the edge of traditional geometry and incorporates a touch of combinatorics. It studies discrete sets of points, lines, curves and other familiar objects but often with an emphasis on various arrangements of those elements. Counting or optimizing configurations of those pieces is also an important component. This book...

Cover of the book Exploring Discrete Geometry by Thomas Q. Sibley, part of the Anneli Lax New Mathematical Library (Vol. 56), published by MAA Press, an imprint of the American Mathematical Society. The cover features two colorful geometric illustrations: an icosahedron on the left and a subdivided tetrahedron on the right, both composed of red, blue, green, and white triangular faces. The MAA Press and AMS logos are at the bottom.

Metric Algebraic Geometry

Metric Algebraic Geometry aims to join methods and ideas of (metric) differential geometry with its (real) algebraic counterpart, with a common goal a variety of practical applications in optimization, modeling and analyzing statistical data, machine learning and computer vision. An ambitious goal indeed. The motivating observation is that many problems in those applications can be approached using polynomial equations...

Book Cover of Metric Algebraic Geometry to accompany review of this book

Algebraic Geometry: Notes on a Course

David Murphy is Professor of Mathematics at Hillsdale College in Michigan. His area of expertise is algebraic geometry.

Algebraic Curves and Surfaces

The geometry of algebraic curves and surfaces is a wide and venerable subject, and there are many monographs and textbooks aimed to graduate students and experienced researchers. The novelties of the book under review include a historical overview of the classification theorem of algebraic surfaces, from the classical results of the Italian school of Castelnuovo and Enriques to the methods of the French...

Abelian Varieties over the Complex Numbers

Abel’s far-reaching generalization for hyperelliptic integrals (Abelian integrals) of Euler’s addition theorem for elliptic integrals (a finite sum of such integrals may be written as g such integrals, where g is the genus of the corresponding algebraic curve, save some logarithmic integrals), still resonates throughout the history of our science. The geometry and arithmetic of abelian varieties is a very active area of...

A Concise Introduction to Algebraic Varieties

For a quick and reader-friendly short introduction to algebraic varieties this new book could be a nice choice for a one-semester course. With a minimum of commutative algebra background, summarized in one appendix, and a bare minimum of point-set topology, this textbook covers the basics of abstract algebraic varieties over an algebraically closed field. From...

K3 Surfaces

K3 Surfaces is, unsurprisingly, a book about K3 surfaces. The book is particularly focused on the proof and applications of the Torelli-type theorem for K3 surfaces, which allow for isomorphism classification for these objects. As a translation of Kondō’s original publication on this topic to English from Japanese, some updates were made and two chapters were...

Cover of 'K3 Surfaces' by Shigeyuki Kondō, featuring a minimalist design with the title and author's name prominently displayed on a solid background.

Rational Points on Curves Over Finite Fields

As with many of the wonderful books that Serre has written, this one started with the notes of a series of lectures that Serre gave, this time during the Fall Semester of 1985 at Harvard University. The handwritten notes taken by F. Q. Gouvêa in 1985 circulated in photocopies or scanned pdf files, frequently cited...

Alt text: Book cover titled "Rational Points on Curves over Finite Fields" by Jean-Pierre Serre, with contributions by Everett Howe, Joseph Oesterlé, and Christophe Ritzenthaler. The cover features a clean design with a white central panel bordered by yellow-orange bands. The series title "Documents Mathématiques" appears at the top, and the publisher "Société Mathématique de France" is listed at the bottom. A small decorative illustration of books and mathematical objects is centered below the title.

Perfectoid Spaces: Lectures from the 2017 Arizona Winter School

This book is an expanded and edited compilation of lecture notes from the 2017 Arizona Winter School on perfectoid spaces. The aim of the book and the corresponding winter school is to give graduate students in number theory a place to start learning about (and even doing research into) this new and exciting topic. I...

Cover of the book "Perfectoid Spaces: Lectures from the 2017 Arizona Winter School," part of the Mathematical Surveys and Monographs series (Volume 242) by the American Mathematical Society. The design features a gray background with an orange vertical sidebar on the left. The title and contributors—Bhargav Bhatt, Ana Caraiani, Kiran S. Kedlaya, Jared Weinstein, and editor Bryden Cais—are listed in blue text, with an introduction by Peter Scholze.