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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

1 vote
0 answers
117 views

Embedded associated points of a cokernel sheaf

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 …
shamovic's user avatar
  • 431
2 votes

algebraic closure of a subgroup of GL

Furthermore the linear span of $\Gamma$ is not contained in $GL(n,\mathbb{C})$. So you have to ask, where is it Zariski closed?
shamovic's user avatar
  • 431
3 votes
3 answers
548 views

Castelnuovo-Mumford Regularity of Ideals of Maximal Minors

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 …
shamovic's user avatar
  • 431
2 votes
0 answers
120 views

Generalized Hurwitz Spaces

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 $ …
shamovic's user avatar
  • 431
2 votes
0 answers
134 views

Lifting of Commuting Maps of Vector Bundles

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 …
shamovic's user avatar
  • 431
19 votes
1 answer
2k views

Is every projective space curve a set-theoretic intersection of two surfaces? What is known ...

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( …
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  • 431