1
vote
1answer
107 views

divisors on $\overline{\mathcal{M}}_{g,n}$ that are trivial on certain $F$-curves

Inside the moduli space of curves $\overline{\mathcal{M}}_{g,n}$ one can distinguish two classes of $F$-curves isomorphic to $\mathbb{P}^1$: those of type $\overline{\mathcal{M}}_{0,4}$, and those of ...
2
votes
1answer
269 views

Picard/cohomology lattice of surfaces of low degree in $\mathbb P^3$

Let $S_{d>3}\subset\mathbb{P}^3_{\mathbb{C}}$ be a smooth surface of degree $d$. What is known (where to read?) about the Picard/cohomology lattice for small d? e.g. for $d=4$ the cohomology ...
3
votes
0answers
237 views

On generators of the Picard group of a projective smooth surface over a finite field

Let $X$ be a smooth projective surface over a finite field $k=\mathbb{F}_q$. Let us first review the proof of the finite generation of $Pic(X)$ (notice that the proof is valid for any smooth ...
2
votes
0answers
315 views

A motivic complex

By definition, Voevodsky's motivic complex (an object of his $DM^{eff}_-$) is a complex of sheaves with transfers whose cohomology sheaves are homotopy invariant. Now, I consider the complex (of ...
11
votes
6answers
1k 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 ...