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Results tagged with moduli-spaces
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user 404
Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.
4
votes
Line bundles on moduli spaces
In general Cohomology is a tool to linearize global properties (just like calculus is a tool to linearize local properties).
Line bundles are elements in the (probably) most important cohomology gro …
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1
vote
What is an example of a function on M_g?
Any odd theta characteristic is realized in the canonical system as a hyperplane (dualizing system if you want to work on the boundary too). So, for each curve you get a set of N=(2^g-1)(2^(g-1)) poin …
- 4,394
4
votes
Accepted
Algorithms for semistable reduction of families of curves
If your curves are in P^n (specifically in P^2 - as in your example), I think there is something you can do: project your curves from a general P^{n-2} to P^1. This means that you
are now looking for …
- 4,394
13
votes
Accepted
Moduli space of K3 surfaces
I think you are looking for this
http://arxiv.org/pdf/math/0506120
which is the same as:
Rizov, Jordan Moduli stacks of polarized $K3$ surfaces in mixed characteristic. Serdica Math. J. 32 (2006), …
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2
votes
Moduli of smooth curves
Is Arbarello's 74 paper (specifically, theorem 3.27 there) Weierstrass points and moduli of curves an easy enough argument ?
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3
votes
Accepted
Genus 2 curves vs Abelian surfaces
The analytic solution is easy enough to describe: Compute the gradients of the Theta function at the six odd 2-torsion points, and projectivize these gradients. You now have six points on the projecti …
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8
votes
Introductory text for the non-arithmetic moduli of elliptic curves
Clemens's A scrapbook of complex curve theory, chapters 2,3
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2
votes
Why is the Hodge class of \bar{M_g} big and nef?
For nef you can do the following: Take a map from some Hurwitz scheme to \bar{Mg}. Then any test curve in \bar{Mg} pulls to one in the Hurwitz scheme. You now compute the integral of the hodge class o …
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3
votes
Accepted
How does one intersect non-transverse divisors on Mg-bar.
Both questions reduce to showing the 2-fold intersection of D_1 is a the closure of the locus of
genus g-2 curve with two elliptic tails.
The first question follows from this claim by induction and u …
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12
votes
Accepted
Moduli spaces of complex curves as algebraic varieties
The classical (pre Deligne-Mumford) approach is to map $\mathcal{M}_g$ into $\mathcal{A}_g$ using the Torreli map. Whereas the classical way to see that $\mathcal{A}_g$ is quasi-projective is to defin …
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5
votes
A historical question: Hurwitz, Luroth, Clebsch, and the connectedness of $\mathcal{M}_g$
Harris and Morrison point you (after stating the theorem in 1.5.4) to Clebsch's Zur Theorie der Rieman'schen Flachen Math Ann. 6 216-230, 1872. My German is not that good, but section 2 seems convinci …
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