5
votes
1answer
150 views

Reference request: maps between moduli spaces

I want to understand the relationship between moduli spaces as we vary the different parameters. I'll focus on the moduli space ${\mathcal M}_{g,n}(X,\beta)$ of stable maps from genus $g$ curves with ...
3
votes
1answer
243 views

notion of stability in a category

This is a question in general sense, but answers about specific examples are also welcome. Why do we need the notion of stability of objects in a category. If we've a subcategory of stable objects, ...
4
votes
1answer
352 views

“extend a functor”

Hi, I have probably a basic question. I have a functor $F: Sch \rightarrow Set$, an algebraic stack $M$ with a "universal family" $G\rightarrow M$ and a representability property like this: for every ...
8
votes
1answer
560 views

Non-representable functor, representable on locally Noetherian schemes?

What is an example of a functor $F : \mathbb{C}\text{-Sch.} \to \text{Sets}$ with the property that the restriction of $F$ to locally Noetherian $\mathbb{C}$-schemes can be represented by a locally ...
2
votes
0answers
158 views

How to characterize good “models” of a category

Let ${\bf Cat}$ denote the category of small categories. Recall that for a category $\mathcal{C}$ and a functor $F\colon\mathcal{C}\to{\bf Cat}$, the Grothendieck construction of $F$, which I'll ...