All Questions
Tagged with geometric-invariant-theory moduli-spaces
12 questions with no upvoted or accepted answers
6
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0
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679
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Learning about moduli spaces of sheaves
I am a Ph.D. student and starting a side project with a fellow student on Moduli spaces. Our plan was to start with the book on Invariants and Moduli by Mukai (starting from chapter 5) and use the ...
- 345
6
votes
0
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591
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Affine GIT quotients and the excursion algebra in Fargues–Scholze
Some background:
Let us fix a non-archimedean local field $E$ with residue characteristic $p$, and let $G$ be some connected reductive group over $E$. In [FS, §VIII.1.1] the authors define a moduli ...
- 787
5
votes
0
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347
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Good quotients and coarse moduli spaces
I started study the moduli space theory, by Newstead's book ''Lectures on moduli problems and orbit spaces". Theorem 3.21 says that given a variety $X$ and a line bundle $L$ over $X$, then for any L-...
- 558
4
votes
0
answers
117
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Complexifed Gauge action on determinant line bundle and change of metric
Within the GIT setup for Hermitian-Einstein connection, Donaldson exhibited a holomorphic line bundle over $\mathcal{A}$ the space of unitary connections such that its cutvature equals $−2πi\Omega$ ...
- 789
4
votes
0
answers
520
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A quotient stack question
Let $X$ be a proper Deligne-Mumford stack, whose normalization, $X'$, is a global quotient stack (that is, a stack of the form [W/GL_n],where W is an algebraic space) with a projective scheme as a ...
- 73
3
votes
0
answers
364
views
Choosing a group action to do GIT of hypersurfaces
When studying GIT stability of hypersurfaces $d$ of $\mathbb P^n$ we look at the Hilbert Scheme $H=\mathbb P^N$ parametrizing homogeneous polynomials $f_d(x_0,\ldots,x_n)$ of degree $d$. There is ...
- 31
2
votes
0
answers
93
views
How are moduli spaces related to geometric complexity theory?
I am interested in understanding the relationship between moduli spaces and geometric complexity theory (GCT).
Relation between moduli spaces and GCT:
How are moduli spaces related to geometric ...
- 29
2
votes
0
answers
117
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GIT semi-stability on graded Artinian local $\Bbbk$-algebras
Let $\Bbbk$ be a algebraically closed field of characteristic zero. A graded Artinian local $\Bbbk$-algebra is $(A,\mathfrak{m},\bigoplus A_i)$ such that $(A,\mathfrak{m})$ is an Artianian local $\...
- 930
2
votes
0
answers
218
views
Level n-structure as defined by Mumford in GIT
In Mumford's GIT, the definition of level $n$ structure ($n \geq 2)$ is $2g$ sections $\{\sigma_1, \dots, \sigma_{2g}\} : S \rightarrow A$ such that two conditions hold: (i) For geometric points the ...
- 419
1
vote
0
answers
86
views
What is the functor of points of the moduli scheme of stable sheaves?
Let $\Bbbk$ be an algebraic closed field of characteristic zero. Let $(\mathrm{Sch}/\Bbbk$ denote the category of locally Noetherian schemes. Let $B$ be a projective scheme over $\Bbbk$. Let $L$ be an ...
- 930
1
vote
0
answers
153
views
Descent of projective bundles
A problem studied in GIT is the descending of vector bundles (or more in general coherent sheaves) to quotients.
It is a result of Kempf that whenever we have a vector bundle over a quasiprojective ...
- 297
1
vote
0
answers
189
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Mumford's claim on the quasi-projectiveness of the coarse moduli of ppav over $\mathbb{Z}$
In paragraph 3 of chapter 7 of Mumford's Geometric Invariant Theory, the author proves that the coarse moduli space $A_{g,d,n}$ of abelian varieties of dimension $g$, with a degree $d^2$ polarization ...
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