# Tagged Questions

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### Stability of analytic Zariski structures

Noetherian Zariski structures are introduced by Hrushovski and Zilber.(1996)
An analytic Zariski structure is a generalization of Noetherian Zariski structures, introduced by Zilber and Peatfield.
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298 views

### Derived categories of singular varieties

Given my limited knowledge on derived categories, all the results on derived categories of complex of bounded sheaves are build upon smooth varieties, and people literally avoid singular case (as in ...

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### Existence of constant scalar curvature Kahler metrics on projective manifolds

It is well known that the blow-up of $\mathbb P^2$ in one or two points does not accept a Kahler-Einstein metric. Kahler-Einstein metrics are particular cases of constant scalar curvature Kahler ...

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135 views

### Ampleness on the P^1 bundle over Siegel threefold

I am looking at the Shimura variety for $\mathrm{GSp}_4(\mathbb Q)$, with hyperspecial level structure at $p$. Let $X$ denote the special fiber over $\mathbb F_p$. For simplicity, let us pretend ...

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290 views

### Higgs bundle and stable bundle

Let $(E,\phi)$ be a $G$-Higgs bundle $\phi\in H^{0}(X,ad(E)\otimes D)$ where $D$ is a divisor on X.
I suppose that $(E,\phi)\in \mathcal{M}^{ani}$ the anisotropic locus.
In particuler, this bundle ...

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**1**answer

229 views

### Direct sum of two stable bundles of same slope

How to prove that the direct sum of two stable vector bundles of the same slope over a smooth curve is a semistable bundle?

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702 views

### What's “bad” about unstable sheaves?

To construct a (coarse or fine) moduli space that is separated, one usually throw away some class of the object in question. For moduli of sheaves people talk about (semi-)stability. A coherent sheaf ...

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417 views

### Moduli spaces of vector bundles and stability conditions

Let $C$ be an algebraic curve. One of the easiest examples of stabilty functions is
$$Z:Coh(C)/ \{ 0 \} \rightarrow \overline{\mathbb{H}};\ \ \ \ Z(E):=-deg(E)+i\cdot rk(E).$$
This induces the ...