3,685 reputation
1233
bio website math.jussieu.fr/~diverio
location Paris
age 35
visits member for 4 years, 7 months
seen 23 hours ago

I am a researcher in complex analytic and algebraic geometry at the Institut de Mathématiques de Jussieu.


Apr
22
comment Is dimension invariant under blow-ups?
This is certainly true if $X$ is a locally Noetherian integral scheme and you blow-up a non-zero quasi-coherent sheaf of ideals. In this case, the blow-up morphism is proper and birational, and $X'$ integral. Finally, if $f\colon Z\to Y$ is any proper birational morphism, where $Y$ is a locally Noetherian integral scheme, then $\dim Z=\dim Y$.
Mar
30
revised Examples of Brody hyperbolic affine varieties which are not Kobayashi hyperbolic
added a quasi-projective example, a reference to a book of S. Lang, a hint where to look at in order to answer the question
Mar
3
revised Applications of Liouville's theorem
added the "teaching" tag
Mar
3
comment Bertini theorem for big divisors and klt pairs
Wilson's theorem is Theorem 2.3.9 in Lazarsfeld's book "Positivity in algebraic geometry I". The corollary Hacon is talking about is Proposition 11.2.18 in "Positivity in algebraic geometry II".
Mar
3
revised Why can we not always take a Kähler class to be in rational cohomology?
modified the last part following the comments of ACL
Mar
3
comment Why can we not always take a Kähler class to be in rational cohomology?
@ArtiePrendergast-Smith: it was my pleasure! I didn't want to "steal" your answer, but at some point I saw that you weren't answering and so... Anyway, maybe I shall modify my $\mathbb Q^2$ in $\mathbb Q^3$, to avoid the problem pointed out by ACL.
Mar
3
awarded  Nice Answer
Mar
2
comment Why can we not always take a Kähler class to be in rational cohomology?
Ahhhhh ok! Now I see the point!! Yes, indeed! My exemple was somehow artificial just to explain what was going on... You are right!
Mar
2
comment Why can we not always take a Kähler class to be in rational cohomology?
Right, there is no pure Hodge structure of weight 2 with $\dim V^{1,1}_\mathbb R=1$. But I am still missing something in order to understand your comment above...
Mar
2
comment Why can we not always take a Kähler class to be in rational cohomology?
@ACL. Sorry but I am not sure I understand well your comment... The solution to what? And what do you mean about the $V^{01}$? Cheers, Simone.
Mar
2
revised Why can we not always take a Kähler class to be in rational cohomology?
slight change following YangMills comment.
Mar
2
revised Why can we not always take a Kähler class to be in rational cohomology?
slight change following YangMills comment.
Mar
2
comment Why can we not always take a Kähler class to be in rational cohomology?
Dear YangMills, I think this is a misunderstanding: I was speaking about a general dense subset, saying in parenthesis to keep in mind the case of $V_\mathbb Q$. But I admit that the way I wrote it can be misleading. I try to fix it.
Mar
1
answered Why can we not always take a Kähler class to be in rational cohomology?
Feb
27
comment Why can we not always take a Kähler class to be in rational cohomology?
@Artie Prendergast-Smith. I think you should write a (short) answer instead of a comment, because this comment is indeed the answer! The OP just want to know where he is wrong in his reasoning, and not really examples of Kähler non projective compact complex manifolds (it seems to me that he is aware of this)!
Feb
18
awarded  Popular Question
Feb
18
comment Extending holomorphic forms
Did you take a look at this paper arxiv.org/pdf/1202.3243.pdf ?
Feb
16
revised Complex manifolds with trivial canonical bundle
added 39 characters in body
Feb
16
revised Complex manifolds with trivial canonical bundle
Added a warning in response to the OP comment
Feb
16
answered Complex manifolds with trivial canonical bundle