Sándor Kovács
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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.