bio | website | math.jussieu.fr/~diverio |
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location | Paris | |
age | 35 | |
visits | member for | 4 years, 8 months |
seen | 9 hours ago | |
stats | profile views | 3,076 |
I am a researcher in complex analytic and algebraic geometry at the Institut de MathÃ©matiques de Jussieu.
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. |
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 ? |