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Nov
25 |
comment |
relation between algebraic geometry and complex geometry
A projective variety, even smooth, is, as a a rule, not locally $\mathbb C^n$ with Zariski topology. |
Dec
16 |
awarded | Yearling |
Jul
2 |
awarded | Curious |
Dec
23 |
comment |
To what extent does the branch locus determine the covering (Chisini's conjecture)?
And yes, I'm interested in positive results, and I am not sure the suggested construction will yield counterexamples. |
Dec
23 |
comment |
To what extent does the branch locus determine the covering (Chisini's conjecture)?
@Jason: if the surface $X$ is irreducuble, then the homomorphism $\pi_1(\mathbb P^2\setminus S,p)\to \mathrm{Aut}(f^{-1}(p))$ is automatically surjective. |
Dec
23 |
asked | To what extent does the branch locus determine the covering (Chisini's conjecture)? |
Dec
16 |
awarded | Yearling |
Nov
25 |
comment |
Is the Picard number bounded by $b_2$ in positive characteristic?
A minor correction: in char 0, $\rho(X)\le b_2(X)$, not necessarily strictly less. |
Nov
24 |
revised |
arctan of a square root as a rational multiple of pi
corrected tags |
Nov
24 |
suggested | approved edit on arctan of a square root as a rational multiple of pi |
Nov
23 |
comment |
rational map becomes a morphism after blow-ups
@Jason: that's right, of course, but I believe the OP meant blow-ups with smooth centers (and rational map of smooth varieties). |
Nov
23 |
awarded | Informed |
Nov
16 |
accepted | Self-dual surfaces in $\mathbb P^3$ with isolated singularities |
Nov
16 |
comment |
Self-dual surfaces in $\mathbb P^3$ with isolated singularities
@Francesco: thank you |
Nov
16 |
revised |
Self-dual surfaces in $\mathbb P^3$ with isolated singularities
a TeX error |
Nov
16 |
asked | Self-dual surfaces in $\mathbb P^3$ with isolated singularities |
Sep
6 |
comment |
On Serre's twisting sheaf
If $Y$ is a cone, then all these maps are surjective. If the Zariski tangent space at at least one point of $Y$ has dimension $n$, then $H^0(\mathcal O_{\mathbb P^n}(1))$ surjects on $H^0(\mathcal O_Y(1))$ (I am not sure about $\mathcal O(j)$ with $j>1$). I would not say these results are general enough. |
Sep
5 |
answered | References on complete intersections in Grassmanian |
Aug
18 |
comment |
General curves of genus 3 as plane sections of Kummer surfaces
Sorry, do you really mean «generically injective»? If a quartic has automorphisms, then the mapping in question from $(\mathbb P^3)^*$ to $M_3$ cannot be generically injective. Did you actually mean «has 3-dimensional image»? |
Aug
18 |
comment |
General curves of genus 3 as plane sections of Kummer surfaces
Thank you, interesting indeed. Is this problem open even for the case of smooth quartics? |