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 Yearling
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  • 84 votes cast
Jan
1
comment Will any two linearly equivalent ample divisors on an abelian variety intersect?
I would add tht if two divisors on a smooth variety have a non-empty intersection, then codimension of this intersection is at most 2. This has nothing to do with their ampleneess.
Dec
31
comment Explicit form of certain polynomials and intersection of curves
You may want to shift the $(d)$ in the right-hand side eastward: if $d\ne 0$, then $\mathcal I_X$ is not a subsheaf of $(\mathcal I_C+\mathcal I_D)(d)$. (Sorry for the edit.)
Dec
30
accepted Self-dual plane curves
Dec
30
revised Self-dual plane curves
added 3 characters in body
Dec
30
comment Self-dual plane curves
@Jason: of course! I mean cuspidal, thank you for the correction.
Dec
30
asked Self-dual plane curves
Dec
16
awarded  Yearling
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