bio  website  math.jussieu.fr/~diverio 

location  Paris  
age  35  
visits  member for  4 years, 5 months 
seen  21 mins ago  
stats  profile views  2,977 
I am a researcher in complex analytic and algebraic geometry at the Institut de MathÃ©matiques de Jussieu.
1h

revised 
Confusion with global sections of reflexive sheaves
edited body 
1h

revised 
Examples of Brody hyperbolic affine varieties which are not Kobayashi hyperbolic
added a quasiprojective 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?
@ArtiePrendergastSmith: 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 PrendergastSmith. 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 