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Results tagged with moduli-spaces
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user 5259
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.
7
votes
1
answer
457
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Some questions on moduli of stable maps
Let $\overline{M}_{0,k}(\mathbb{P}^n,d)$
denote the moduli space of genus zero degree $d$ stable maps with $k$ marked points. This is an orbifold of expected dimension. Let $\overline{U}_{0,k}(\ma …
3
votes
2
answers
405
views
Moduli space of stable maps into very ample hypersurfaces!
Let $X$ be a smooth complex projective variety and $L$ be some ample divisor.
For a holomorphic map $u:\Sigma \to X$, we define its degree to be $deg(u^*L)$.
Question: For a given positive integer $M …
3
votes
1
answer
245
views
Intersection theory on M_{g,n}
Is there a paper\book that lists the top intersections of Hodge classes and tautological classes on $\overline{\mathcal{M}}_{g,n}$ for small $g$ and $k$, e.g. $g=2,3$ and $k=0,1,2$ ?
3
votes
0
answers
185
views
Abstract VFC vs. what people actually use for Quintic 3-fold
Moduli space of genus $0$ degree $d$ maps in a quintic Calabi-Yau threefold $X$, written as $\overline{\mathcal{M}}_{0,0}(X,[d])$, can be embedded in the corresponding moduli space of $\mathbb{P}^4$, …
16
votes
4
answers
3k
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Moduli space of genus 2 curves
Does any body know any reference in which the geometry of compactified moduli space of genus two curves ( Which is a three dimensional variety/stack/...) has been studied?
2
votes
Deformation long exact sequence of GW theory in the analytical setting
In addition to the nice description of Jason in the comments,
there is a fairly detailed description of the deformation long exact sequence in Section 3.2 of the article of Siebert-Tian in "Symplecti …
6
votes
1
answer
285
views
Deformation long exact sequence of GW theory in the analytical setting
Let $f\!=\!(u\colon (\Sigma,p_1,\ldots,p_k) \to X)$ be an element of the moduli space of genus $g$ $k$-marked degree $A$ $J$-holomorphic maps $\mathcal{M}_{g,k}(X,A,J)$. For simplicity assume $C=(\Sig …
9
votes
2
answers
4k
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Reference request: moduli spaces of vector bundles
I am trying to study the moduli spaces of holomorphic vector bundles quickly, and I'm primarily interested in understanding:
Why and where the stability condition is used.
How are the moduli spaces …