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Results tagged with ag.algebraic-geometry
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user 18263
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
4
votes
0
answers
86
views
Efficient CW structures on squarefree semi-algebraic set
General Setup
Given a collection of $k$ polynomials (with real coefficients) in $n$ real variables, say $f_i(x_1,\ldots,x_n)$, let $V \subset \mathbb{R}^n$ correspond to those $x$-values for which ev …
- 15.5k
5
votes
Accepted
Simplicial complex construction from given Betti numbers?
One way to make things "minimal" (given the lack of any further information) is to construct a simplicial complex whose cup products are all trivial, so the (co)homology generators don't interact with …
- 15.5k
11
votes
Why Cohen-Macaulay rings have become important in commutative algebra?
I'm no expert on the evolution of Cohen-Macaulay rings, so I will leave that part of your question for those who actually know their history.
On a high level, Cohen-Macaulay rings are wonderful prec …
- 15.5k
5
votes
Decomposition vs filtration vs stratification
At the risk of sounding (oxy?)moronic, I'd say that the term "stratification" is locally standard. Meaning, there exist (at least) three communities which agree internally on what the term means, but …
- 15.5k
16
votes
Taking "Zooming in on a point of a graph" seriously
I haven't seen any Calculus books take this approach. Possibly, this is because it is not clear how to proceed in the case of functions that are not polynomials. Consider even the really nice function …
- 15.5k
16
votes
1
answer
359
views
Moduli space of boundary maps with prescribed chain and homology groups?
Let $R$ be a reasonable ring (maybe I mean a PID, or $\mathbb{Z}$, and when sufficiently desperate, a field). Now consider fixed sequences $C_n$ and $H_n$ of $R$-modules, which are tame in every possi …
- 15.5k
12
votes
Can we define Whitney stratification algebraically?
There is a purely algebraic characterisation of Condition (B) due to Le and Teissier, see Proposition 1.3.8 of the paper
Lê Dũng Tráng; Teissier, Bernard, Limites d’espaces tangents en géométrie analy …
- 15.5k