Why study Algebraic Geometry? - Mathematics Stack Exchange
2012年12月10日 · $\begingroup$ @GustavoBandeira: since the subject is so broad, you may approach it from different perspectives. . The complex geometry approach requires you know enough differential geometry (so rigorous real and complex analysis and differentiable manifolds), the purely algebraic approach requires a good mastery of abstract algebra up to commutative …
reference request - Best way to learn Algebraic Geometry?
Reid's Undergraduate Algebraic Geometry, Chapter I of Hartshorne's Algebraic Geometry and Volume I of Shafarevich's Basic Algebraic Geometry all cover material of this kind. Modern algebraic geometry begins with the study of schemes, and there it is important to have a thorough understanding of localisation, local rings, and modules over them.
What is algebraic geometry? - Mathematics Stack Exchange
2019年7月13日 · Algebraic geometry is about dealing with systems of polynomial equations. As you may imagine, this is much ...
algebraic geometry - Learning schemes - Mathematics Stack …
$\begingroup$ IMHO, the typical very talented math student should still expect to need a long time to learn algebraic geometry, probably much longer than she might expect from past experience (I certainly did, and if I remember right, David Eisenbud himself described as much during his outgoing address to the AMS).
Path to Basics in Algebraic Geometry from HS Algebra and Calculus?
Learn Basic Algebraic Geometry: the most important thing at first is to get what is all about, i.e. how loci defined by solutions to systems of polynomial equations generalize to abstract algebraic varieties and their regular and rational morphisms: An Invitation to Algebraic Geometry by K. E. Smith et al. and Undergraduate Algebraic Geometry ...
general topology - Where to start with Algebraic Geometry ...
I'm looking into studying Algebraic Geometry alongside some Algebraic Topology and was wondering what book would be useful. I was looking along the lines from Igor's Basic Algebraic Geometry, Cox, Little and O'Shea's Ideals, Varieties, and Algorithms, and Justin Smith's Introduction to Algebraic Geometry.
Famous papers in algebraic geometry - Mathematics Stack Exchange
2012年6月21日 · Serre's Faisceaux Algébriques Cohérents (=FAC) has the unique status of being: . a) Arguably the most important article in 20-th century algebraic geometry : it introduced sheaf-theoretic methods into algebraic geometry, including their cohomology, characterization of affine varieties by vanishing of said cohomology for coherent sheaves, twisting sheaves …
algebraic geometry - How is Category Theory used to study …
2018年2月20日 · More generally, solution sets of polynomial equations (and more generally, algebraic varieties) are a central study object of algebraic geometry. As differential equations are central to all areas of physics, I assume that there have been made a lot of attempts to generalise these ideas to solution sets of these.
algebraic geometry - Why study schemes? - Mathematics Stack …
2012年1月16日 · This idea goes back to Weil, and it was introduced in algebraic geometry for the same reason that general manifolds were introduced to replace the study of embedded manifolds in Euclidean space. This allows gluing constructions, without having to check whether the resulting space is embedded in an affine or projective space.
algebraic geometry - What *is* affine space? - Mathematics Stack …
2015年7月6日 · The geometry in these two planes is completely the same. One is simply a translation of the other. But the first we would consider as a subspace of the vector space $\mathbb{R}^3$ and the second we wouldn't consider if we wanted to work in a completely algebraic setting.