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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.

1 vote

An application of the Base Change Theorem to the moduli space of sheaves

I cannot comment due to reputation and haven't done the computations, but I see two possible problems: usually one has a spectral sequence $(R^if_{*})(\mathcal{E}xt^j(M,N)) => \mathcal{E}xt_f^{i+j}( …
Bernie's user avatar
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3 votes
0 answers
151 views

Moduli space with exceptional Mukai vector and tangent spaces at strictly semistable bundles

Assume we work (over $\mathbb{C}$) on a polarized K3 surface $(X,L)$ with a line bundle $M$ on $X$ such that $M^2=-6$ and $ML=0$ as well as $h^0(M)=h^2(M)=0$ and thus $h^1(M)=1$. Then $E=\mathcal{O}_X …
Bernie's user avatar
  • 1,025
2 votes
1 answer
221 views

What finite groups are stabilizers in Kirwan's desingularization construction?

Assume $X$ is a smooth projective curve of genus $g\geq 3$ over $\mathbb{C}$ and let $M$ be the (singular) moduli space of semistable rank two vector bundles with trivial determinant on $X$. Then ther …
Bernie's user avatar
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