All Questions
Tagged with divisors ac.commutative-algebra
8 questions
15
votes
6
answers
2k
views
Seeking Noetherian normal domain with vanishing Picard group but not a UFD
Once again, the question says it all.
My motivation is the article on factorization I am writing. I want to explain (as well as to understand!) why for normal Noetherian domains of dimension greater ...
- 65.4k
5
votes
1
answer
359
views
Computations of divisor class monoids
Let me first recall some definitions from the very first pages of Bourbaki, Commutative Algebra, Chapter 7, "Divisors".
Let $A$ be a (commutative) domain, $K$ its field of fractions. A ...
- 26.1k
4
votes
1
answer
2k
views
On Q-Cartier Divisors
I have my question on Q-Cartier Weil divisor.
People say $D$ is Q-Cartier divisor if $nD$ is Cartier for some $n \geq 1$. Especially for $n > 1$, I have never seen the `rigorous' definition of $...
- 781
3
votes
0
answers
342
views
Hypersurfaces with Gorenstein singular loci
Recall that a hypersurface $D$ in a complex manifold $X$ is called a free divisor if the Lie algebroid $\mathcal{T}_X(-\log D)$ of vector fields tangent to $D$ is locally free. This condition is ...
- 126
1
vote
0
answers
120
views
Question about Local Henselian Rings
I have a question regarding properties/characterizations of local Henselian rings exploited in M. Artin's article "On Isolated Rational Singularities of Surfaces":
Here the relevant excerpt:
Remark: ...
- 5,966
1
vote
0
answers
83
views
lift sections on a thickened curve
Let $X$ a curve over an algebraically closed field $k$ and $D$ a divisor on X.
Fix an integer $N$ and a closed point $x$ on $X$, we assume that $\deg(D)$ is big enough such that we have a surjective ...
- 3,472
0
votes
1
answer
147
views
Are maps into a smooth curve equivalent to relative effective Cartier divisors?
Let $X$ be a smooth curve and $S$ an affine scheme, both over an algebraically closed field $k$.
Given a morphism $f : S \to X$, is it true that the graph morphism $\Gamma_f : S \to X \times S$ is a ...
- 426
0
votes
0
answers
130
views
Is a closed subsecheme contained in a Cartier divisor?
Let $X$ be a variety over a field $k$. For a closed subscheme $Z\hookrightarrow X$ and a closed point $x\in X$ such that $\text{codim}_XZ \geq 1$ and $x\notin |Z|$, is there an effective Cartier ...
- 349