Foundations of Algebraic Geometry Class 37
نویسندگان
چکیده
I prefer to start any topic with a number of examples, but in this case I’m going to spend a fair amount of time discussing technicalities, and then get to a number of examples. Here is the main message I want you to get. Differentials are an intuitive geometric notion, and we’re going to figure out the right description of them algebraically. I find the algebraic manifestation a little non-intuitive, so I always like to tie it to the geometry. So please don’t tune out of the statements. Also, I want you to notice that although the algebraic statements are odd, none of the proofs are hard or long.
منابع مشابه
PhD project offering: tropical scheme theory
Tropical geometry has burgeoned in the decade and a half since its coalescence as a field of study. It is a combinatorialization of algebraic geometry, associating to each algebraic variety a so-called tropical variety, a polyhedral complex that is its combinatorial “shadow”. In the simplest cases tropical geometry can be seen as the algebraic geometry over the tropical semiring T = (R ∪ {∞}, m...
متن کاملAlgebraic Geometry over Lie Algebras
What is algebraic geometry over algebraic systems? Many important relations between elements of a given algebraic system A can be expressed by systems of equations over A. The solution sets of such systems are called algebraic sets over A. Algebraic sets over A form a category, if we take for morphisms polynomial functions in the sense of Definition 6.1 below. As a discipline, algebraic geometr...
متن کاملFoundations of Algebraic Geometry Class 41
Here is an explicit question: are all curves (say reduced, even non-singular, finite type over given k) isomorphic? Obviously not: some are affine, and some (such as P) are not. So to simplify things — and we’ll further motivate this simplification in Class 42 — are all projective curves isomorphic? Perhaps all nonsingular projective curves are isomorphic to P? Once again the answer is no, but ...
متن کاملRecursion-Closed Algebraic Theories
A class of algebraic theories called “recursion-closed,” which generalize the rational theories studied by J. A. Goguen, J. W. Thatcher, E.G. Wagner and J. B. Wright in [in “Proceedings, 17th IEEE Symposium on Foundations of Computer Science, Houston, Texas, October 1976,” pp. 147-158; in “Mathematical Foundations of Computer Science, 1978,” Lecture Notes in Computer Science, Vol. 64, Springer-...
متن کامل