All Questions
22,546 questions
7
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What is an example of a function on M_g?
It feels bad talking about a space without knowing a single function on it, hah?
So what is a function on the moduli space of curves, from the geometric point of view?
From the functorial point of ...
- 2,562
27
votes
1
answer
3k
views
Stein Manifolds and Affine Varieties
When is a Stein manifold a complex affine variety? I had thought that there was a theorem saying that a variety which is Stein and has finitely generated ring of regular functions implies affine, but ...
CommunityBot
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7
votes
1
answer
258
views
7
votes
1
answer
1k
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Valuative criterion for properness
Let $f : X \rightarrow Y$ be a finite type morphism of Noetherian schemes. The valuative criterion for properness runs as follows. Suppose that for any DVR $R$ with fraction field $K$ that any $K$-...
- 156k
6
votes
1
answer
1k
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Uniformization in algebraic/arithmetic geometry?
Jonah's question makes me wonder: What is with uniformization in algebraic/arithmetic geometry? E.g. this article by Faltings seems to be about that, the Shimura-Taniyama statement too, Mochizuki ...
CommunityBot
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10
votes
1
answer
2k
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Can the valuative criteria for separatedness/properness be checked "formally"?
Suppose f:X→Y is a morphism of finite type between locally noetherian schemes. The valuative criterion for separatedness (resp. properness) says roughly that f is a separated (resp. proper) ...
- 24.1k
11
votes
1
answer
705
views
a question on function fields
Consider the transcendental extension Q(t) of the field of rationals.
To Q(t) adjoin the root of the polynomial x^5+t^5=1. The resulting
field Q(t)[x] is a radical extension of Q(t). Is it true that ...
CommunityBot
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12
votes
2
answers
2k
views
Non-quasi separated morphisms
What are some examples of morphisms of schemes which are not quasi separated?
- 11.3k
13
votes
5
answers
5k
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Examples and intuition for arithmetic schemes
How should a beginner learn about arithmetic schemes (interpret this as you wish, or as a regular scheme, proper and flat over Spec(Z))? What are the most important examples of such schemes? Good ...
- 15.1k
2
votes
1
answer
355
views
k-th Chow Group and k-th graded part of K_0 ismorphic for DM-stacks?
If X is an algebraic scheme, K_0(X) has a filtration by taking the subgroups generated by coherent sheaves whose support as at most dimension k. The associated graded groups are the quotients, and ...
- 13.6k
4
votes
3
answers
715
views
Is a holomorphic vector bundle on a projective variety locally trivial in the Zariski topology?
By the GAGA principle we know that a holomorphic vector bundle E->X is analitically isomorphic to an algebraic one, say F->X, and by definition F is locally trivial in the Zariski topology. But since ...
- 15.1k
2
votes
0
answers
526
views
How much of math could be taught without using mathematical notation? [closed]
Given that mathematics is not about number, and that it is not even about the cryptic notation used to describe mathematical problems, how much of mathematics could be taught without reference to ...
2
votes
1
answer
167
views
Triviality of the Hodge bundle for a special family of semistable curves
Let g,h be positive integers. Let E be an elliptic curve, C be a genus h curve, and D be a genus g-h-1 curve. Let c,d,e be points on (resp.) C,D, and E.
Let f:CC --> E-e be the family whose fiber ...
CommunityBot
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0
votes
1
answer
485
views
Understanding a lemma in "Loop Spaces and Langlands Parameters" article
First, some background. I was trying to read the article Loop Spaces and Langlands Parameters but I get immediately stuck at Theorem 2.1 in the introduction.
This was actually forward-referring to ...
- 15.1k
4
votes
2
answers
2k
views
Pushforwards of Line Bundles and Stability
I recently finished reading this paper, and was wondering about a couple of things relating to theorem 1, which says that for any curve X there is a curve Y and f:Y->X such that pushforward is a ...
- 280
5
votes
4
answers
666
views
Sections of a divisor on elliptic curve
I'm interested in producing explicit bases for the sections of a line bundle on an embedded genus 1 curve. Let me restrict to the first case that I don't know how to do, so that I can be as concrete ...
- 4,394
3
votes
2
answers
242
views
Vector spaces of singular planar cubics
What is the largest dimensional linear space of singular planar cubics? Is this known?
Think of the space of planar cubics as a PP^9 (parametrized by the coefficients). The discriminant \Delta is ...
- 8,828
7
votes
1
answer
449
views
How does one intersect non-transverse divisors on Mg-bar.
Let Mg-bar be the Deligne-Mumford compactification of genus g curves, and let δ1 be the divisor of degenerate curves of the form `genus 1 meeting a genus g-1 transversely".
Question 1: What ...
- 4,394
2
votes
1
answer
173
views
Projective Curves which are Principal Bundles
I have a very specific question: does anyone know of a (non-trivial) example of a projective curve which is also a homogenous space (or just a principal bundle)? The trivial example being CP^1 = SU(2)/...
- 156k
3
votes
1
answer
320
views
limits of algebraic varieties
I'm looking for a reference which deals with limits of families of algebraic varieties as the degree increases (or at least keywords from this subject).
For the kind of example I have in mind, ...
- 3,022
4
votes
2
answers
759
views
What is the homology of the real coordinate ring of SO(n,R)? Other compact matrix groups?
As someone whose knowledge of cohomology is patchy and picked up on a need-to-know basis, and whose algebraic geometry is even worse, I wondered if someone could help with this question. (I ran into ...
- 25.8k
17
votes
2
answers
3k
views
Are curves with `fractional points' uniquely determined by their residual gerbes?
One makes precise the vague notion of "curve with a fractional point removed" (see for instance these slides) using stacks -- one should really consider Deligne-Mumford stacks whose coarse spaces are ...
CommunityBot
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14
votes
2
answers
989
views
Do orbits and stable loci of group actions have natural scheme structures?
Suppose G is an algebraic group with an action G×X→X on a scheme. Then many of the usual constructions you make when you talk about group actions on sets can be made scheme-theoretically. ...
CommunityBot
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8
votes
2
answers
481
views
Division Algebras as Algebraic Groups
If I'm given a division algebra D with Z(D)=F, then how can I view Dx as an algebraic group defined over F? I'd like to see first how Dx can be given the structure of a variety defined over F, and ...
- 666
3
votes
1
answer
261
views
Over which schemes can there exist non-trivial G_a bundles?
The group scheme G_a here is the one-dimensional additive group.
- 4,949
4
votes
1
answer
321
views
Reverse Langlands transform
What os the meaning of a reverse Langlands transform to which Drinfeld seems to refer?
CommunityBot
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2
votes
2
answers
550
views
Algebraic Geometry in an applied setting?
I just saw this paper recently which mentioned that the optimization on a Grassmanian Manifold can be used to get an achieve an best approximation of a multilinear rank of a tensor (in the sense of a ...
- 8,681
6
votes
1
answer
1k
views
What is Drinfeld's manuscript "Best Dream" (in Russian!) about?
I would like to know what Drinfeld's scanned manuscript "Best Dream" is about: the title makes me curious.
It's in Russian.
- 15.1k
1
vote
1
answer
162
views
Does automatic decomposition of varieties into irreducibles exist?
Varieties decompose uniquely into finitely many irreducibles, and each variety is generated by only finitely polynomials. These two finiteness properties make varieties seemingly "manageable" objects, ...
- 5,243
14
votes
2
answers
882
views
A complex manifold which is quasiprojective in two different ways
Does there exist a complex manifold M which is a quasiprojective variety in two "essentially" different ways? Let me be more specific. I'm looking for a complex manifold M together with two ...
- 5,062
8
votes
1
answer
1k
views
Learning about Galois representations
My goal was to learn about l-adic representations on some example — I'm a newbie in these topics.
Thus take pt = Spec F_q, ...
- 15.1k
8
votes
3
answers
832
views
Why is the Hodge class of \bar{M_g} big and nef?
Let pi: \bar{Mg,1} \to \bar{M_g} be natural projection of compactified moduli stacks of curves and let omega be the relative dualizing sheaf. Then the Hodge class \lambda of \bar{M_g} is the first ...
- 10.5k
11
votes
2
answers
2k
views
Finiteness conditions on simplicial sheaves/presheaves
Could someone give an overview, or just some examples, of "finiteness conditions" for simplicial sheaves/presheaves and/or simplicial schemes? Any answer or comment about this would be interesting, ...
- 13.6k
5
votes
1
answer
332
views
Extending Functions on Closed Submanifolds of C^n
Functions on an algebraic subvariety X of A^n are the same as functions on A^n restricted to X. So the statement that functions on X extend to all of A^n follows by the definition. My question is: ...
- 10.5k
13
votes
6
answers
3k
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Gromov-Witten theory and compactifications of the moduli of curves
Why, from a string theory perspective, is it natural to consider the Deligne-Mumford (resp. Kontsevich) compactification of the moduli of curves (resp. maps [from curves to a target space X]) rather ...
- 2,706
8
votes
1
answer
688
views
Universal covers of domains in complex projective space
The Uniformization Theorem states that the universal cover of a Riemann surface is biholomorphic to the extended complex plane, the complex plane or the open unit disk. Each of these three is a domain ...
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6
votes
1
answer
777
views
Existence of proper regular models for varieties over Q and other global fields
What is known about regular proper models for smooth projective varieties over Q? Results for other global fields would also be interesting, as well as general comments and suggested references for ...
CommunityBot
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6
votes
3
answers
1k
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Is there a software package that does Schubert Calculus computations?
Is there a good software package for doing computations in the cohomology ring of Grassmannians? Things like, I can write down a polynomial in, in fact, special Schubert classes, but it's one where ...
- 4,394
9
votes
1
answer
1k
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Example where you *need* non-DVRs in the valuative criteria
The valuative criterion for separatedness (resp. properness) says that a morphism of schemes (resp. a quasi-compact morphism of schemes) f:X→Y is separated (resp. proper) if and only if it ...
- 10.5k
10
votes
2
answers
944
views
Logarithmic structures on moduli of elliptic curves over Z
I've heard it stated that if you take the moduli of elliptic curves with some level structure imposed (as a moduli scheme over Spec(Z)), there is a logarithmic structure that you can impose at the ...
- 45.7k
2
votes
1
answer
406
views
Are there any criteria for a presheaf which is an etale sheaf to be a sheaf in the fppf topology?
I am happy to hear answers to variants too. For instance, my situation I actually have a sheaf in the smooth topology.
CommunityBot
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9
votes
1
answer
841
views
Limit Linear Series
A linear series on a curve C is a line bundle L together with a subspace V of the global sections of L. Eisenbud and Harris develeoped a theory of limit linear series which explans how (L, V) ...
7
votes
1
answer
2k
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Dualizing sheaf on singular curves
I am trying to understand the stabilization map, which takes a prestable curve (a curve with some marked points, and at worst nodal singularities) and returns a stable curve (a curve with some marked ...
- 45.7k
15
votes
1
answer
2k
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Is there an example of a scheme X whose reduction X_red is affine but X is not affine?
For Noetherian schemes this follows from Serre's criterion for affineness by a filtration argument.
- 5,039
9
votes
1
answer
1k
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Stack with affine stabilizers but not quasi-affine diagonal
Give an example of a stack X with affine stabilizer groups and separated but not quasi-affine diagonal.
Remarks:
1) If X has finite stabilizer groups then the diagonal is quasi-finite and separated, ...
- 716
0
votes
0
answers
2k
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Ignore this question [closed]
This question is a hacky way to create some tags for you to use. Move along.
- 24.1k