# Questions tagged [algebraic-geometry]

The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. This tag should not be used for elementary problems which involve both algebra and geometry.

24,159 questions
Filter by
Sorted by
Tagged with
19 views

### Request for reference for currents

Do you know an introductory book (end of undergraduate/beginning of graduate) about currents in the sense of de Rham? Or even better, a video lecture on that topic? I didn't find it on youtube. Any ...
29 views

Given a vector space $V$ and a quadratic form $q$ on it, we know that the Clifford algebra $Cl(V,q)$ is a graded algebra, which is a property inherited by the Tensor algebra $T(V)$. Unless in the ...
18 views

### First cohomology group of a Lie algebra is isomorphic to $L/[L,L]$?

Let $L$ a Lie algebra on a field of characteristic zero with finite dimension greater than one. I have to show that $H^1(L) \cong L/[L,L]$. Now I write my proof of this statement. First of all I ...
39 views

### Why is $m \geq n$ obvious in Vakil's proof of Noether Normalization (11.2.4)?

This is a very specific part of a classic proof so I had trouble finding duplicates; I apologize if it is one. We have $A$ a finitely generated $k$-algebra which is an integral domain. As such, we ...
18 views

### Specializing Weak Factorization to Birational morphism

The Weak Factorization Theorem tells us that birational map of varieties over field of perfect characteristic which has resolution of singularities can be factored into blow-ups and blow-downs. My ...
19 views

### Line bundles on complete flag varieties independent of isogeny class

Let $G$ be a semisimple connected linear algebraic group over an algebraically closed field $k$. If $G^{sc}$ is the simply-connected cover of $G$ (i.e., the semisimple connected simply-connected ...