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In this question all the varieties are over $\mathbb{C}$. Classic Hurwitz spaces $\mathcal{H}_{g,r}$ are moduli spaces of simple branched coverings $f \colon X \to \mathbb{P}^1$ of degree $d$, where $ …

Assume that we have a vector bundle $\mathcal{F}$ over $\mathbb{P}^d(\mathbb{C})$ that is generated by global sections. Let $\pi \colon \mathcal{O}^n \to \mathcal{F}$ be the associated map that is sur …

I am sorry if this question has been already asked, couldn't find anything similar myself. I have recently recalled this long standing open problem of whether every irreducible curve in $\mathbb{P}^3( …

Hi,I have a reference request regarding associated points of sheaves. I'll be more specific, assume that we are given the following exact sequence on $\mathbb{P}^d_{\mathbb{C}}$: $0 \to \mathcal{O}(-1 …

I have an $m \times 2m$ matrix of linear forms over $\mathbb{C}[x,y,z,w]$. It is of the form $$M = ( x I - A z -B w \mid y I - C z - D w).$$ Here $A,B,C$ and $D$ are $m \times m$ scalar matrices. Let …

Furthermore the linear span of $\Gamma$ is not contained in $GL(n,\mathbb{C})$. So you have to ask, where is it Zariski closed?