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Dec
3
comment $\mathbb{Q}$ divisors on a concrete toric variety: contradiction
I am sorry to hear that what I wrote was confusing. I used the customary language. What you write here is indeed the argument, which I did not include until you asked, because this is standard in this area, but of course if you are new to the area, then you may not have seen it. As I said in the answer above, $\dfrac 12 E$ is not integral even if it is $\mathbb Q$-linearly equivalent to an integral divisor. In other words, here as in the "when-do-divisors-pull-back" answer, it is important to distinguish between divisors and divisor classes. Cheers.
Dec
2
comment $\mathbb{Q}$ divisors on a concrete toric variety: contradiction
There is no pull-back of Weil divisor in this answer. In some sense that's the point. Look at what I wrote about $\mathbb Q$-Cartier divisors in the answer you are linking.
Dec
2
comment $\mathbb{Q}$ divisors on a concrete toric variety: contradiction
Actually it does. I will add some stuff to the answer so you can see it.
Nov
30
revised $\mathbb{Q}$ divisors on a concrete toric variety: contradiction
deleted 55 characters in body
Nov
30
comment $\mathbb{Q}$ divisors on a concrete toric variety: contradiction
You are right, it is $-2L$. But that just means that my original calculation was correct. :)
Nov
27
revised $\mathbb{Q}$ divisors on a concrete toric variety: contradiction
added 169 characters in body
Nov
27
answered $\mathbb{Q}$ divisors on a concrete toric variety: contradiction
Apr
24
answered Cohen-Macaulay rings and Normal rings
Feb
9
revised How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
deleted 382 characters in body
Feb
9
awarded  Commentator
Feb
9
comment How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
OK, I think this indeed does it.
Feb
9
awarded  Yearling
Feb
7
answered pullback of global sections with respect to an automorphism of schemes
Feb
5
comment How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
If you care to explain that argument regarding the norm we can see whether it works. You could post it as another answer with some more details... Cheers!
Feb
5
comment How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
Actually, come to think of it, the definition of $a_1$ and $a_2$ makes no difference. If $a_1+a_2=a$, then $-\tau\left((a_1-\frac a2)P_1\right)=(a_2-\frac a2)P_2$ holds regardless, so this could not have been the problem. But then (again): with what exactly are you having a problem?
Feb
5
comment How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
I've just realized that I did not specify what $a_i$ were. I guess I thought it was obvious, sorry. I edited the answer now. Was that the issue?
Feb
5
revised How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
added 41 characters in body
Feb
5
comment How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
that's the right side. :) What exactly is your question? $\tau$ swaps the points $P_1$ and $P_2$, so this equality follows from the previous one.
Feb
5
comment How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
so where is $a_2$ in that?
Feb
4
comment How to write a divisor: Exercise n 20 pag 285 from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
there is no $a_2$ on the left part. Which equation are you looking at? // Maybe it is true and maybe your norm calculation is OK, I'm just saying that you are stating facts based on some mystery book.