3,730 reputation
1235
bio website math.jussieu.fr/~diverio
location Paris
age 35
visits member for 4 years, 10 months
seen 12 hours ago

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


Aug
2
reviewed Approve Product of Positive Matrices
Aug
2
reviewed Approve What do heat kernels have to do with the Riemann-Roch theorem and the Gauss-Bonnet theorem?
Jul
30
comment Isotrivial families with non-zero Kodaira spencer map
If all fibers are isomorphic, then by the Fischer-Grauert theorem the family is locally trivial. Then, the Kodaira-Spencer map -being "local"- should be zero, isn't it?
Jul
14
awarded  Nice Question
Jul
2
awarded  Popular Question
Jun
12
comment Moduli space of line-bundle holomorphic structures and sections over a Kahler-Hodge manifold
Chern connection with respect to which hermitian metric?
Jun
3
revised Non-cohomological proof that the pullback of an ample bundle by a finite morphism is ample
added the étale hypothesis in order to be more precise.
Jun
3
comment Non-cohomological proof that the pullback of an ample bundle by a finite morphism is ample
@Misaka01034, you can look at any of the books by Demailly about transcendental methods in algebraic geometry (you'll find them freely on his web page)! Anyway for semi-ampleness you don't have a metric characterization (otherwise it would be a numerical property, and it is not), but just that semi-ampleness implies the existence of a smooth metric with positive semi-definite Chern curvature. While bigness is equivalent to posses a (possibily) singular hermitian metric whose curvature current is bounded below by a strictly positive $(1,1)$-form.
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.