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10
votes
0answers
669 views

What is $M_g$ over a finite field, really?

Let $M_{g} \to \mathbb{Z}$ be the coarse moduli scheme of non-singular genus g curves over $\mathbb{Z}$. That is, suppose that $M_{g}$ co-represents the functor $M^{\sharp}_{g} : \text{Sch} \to ...
5
votes
0answers
112 views

global units on moduli spaces of abelian varieties

This is a question from a colleague. Let $A_{g,d,n}$ be the coarse moduli space over $\mathbb Z$ (of the moduli stack, or assume $n\ge3$ if you like) of abelian schemes of relative dimension $g,$ ...
4
votes
0answers
164 views

Is the moduli space of genus three smooth quartics affine?

Non-hyperelliptic curves of genus three are smooth quartics. Is the moduli space of such curves affine? I think this follows from a more general result on smooth complete intersections, but I'm ...
3
votes
0answers
183 views

Stack of vector bundles (on a curve) over a strictly semi-stable point of the moduli space

Consider the stack $Bun_{r,d}^{ss}$ of rank $r$ semi-stable vector bundle of degree $d$ over a fixed curve. There exists also a coarse moduli space $M$ built via GIT. Over the stable locus of $M$ it ...
3
votes
0answers
56 views

Are two “nice” transformation groupoids with the same coarse moduli and isomorphic inertia isomorphic?

Hi! I am stuck with the following question: suppose we have a semisimple connected algebraic group acting on a quasi-affine variety X by closed orbits, and suppose that inertia is flat. Suppose we ...
3
votes
0answers
156 views

Does the Albanese map satisfy Torelli's theorem

Let $M_h$ be the moduli space of canonically polarized varieties with Hilbert polynomial $h$. Let $M_h \to A_g$ be the Albanese map, with $g$ an integer which depends on $h$ and $A_g$ the moduli space ...
2
votes
0answers
202 views

Points of moduli space of semistable sheaves and S-equivalence classes

Let $X$ be smooth projective and connected curve over an algebraically closed field $k$. One knows the description of $k$-valued points of the moduli space $M_X$ of semistable vector bundles of fixed ...
2
votes
0answers
204 views

Is there an algebraic analogue of the degeneration of riemann surfaces in M_g

Degeneration of certain functions such as theta functions or Green's functions in the moduli space $\overline{\mathcal{M}_g}$ of stable curves of genus $g$ has been studied quite alot. The idea is to ...
2
votes
0answers
500 views

Coarse Moduli space of proper Deligne-Mumford stacks

Let F be a finite type proper Deligne-Mumford Stack over a perfect field. Is it true that the coarse moduli space of F is proper?