3,470 reputation
1131
bio website math.jussieu.fr/~diverio
location Paris
age 34
visits member for 4 years, 2 months
seen 8 hours ago

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


Dec
3
comment Stability condition for vector bundles
Hi Angelo, maybe there is something that I am missing, but I cannot understand completely your last argument. Why do you mention the fact that every extension of line bundles on $\mathbb P^2$ splits? In any case, if $E$ fits in a short exact sequence of vector bundles, say with left and right terms respectively $\mathcal O(a)$ and $\mathcal O(b)$, then its Chern classes are given respectively by $a+b$ and $ab$, and one may certainly choose $k$ and $m$ to be not of that form, isn't it?
Nov
18
reviewed Approve Determinant of a determinant
Oct
7
awarded  Yearling
Sep
30
awarded  Explainer
Jul
9
comment Non projective hyperbolic compact complex space
thank you Misha for this insight! so it seems that you think that it is likely that non kähler compact manifolds are all non hyperbolic, right?
Jul
8
revised Non projective hyperbolic compact complex space
added 54 characters in body
Jul
7
asked Non projective hyperbolic compact complex space
Jul
2
awarded  Curious
Jun
20
revised Embedding algebraic surfaces in projective space
edited body
Jun
17
comment Extending holomorphic functions
Connectedness of the complement of $K$ is necessary only if one wants uniqueness of the extended function!
Jun
12
awarded  Necromancer
May
24
revised examples of Kähler manifolds with trivial odd Betti numbers and first Chern classes
fixed typos on the last line
May
18
awarded  Custodian
May
18
reviewed Approve Exact short sequences of vector spaces
Mar
18
awarded  Excavator
Mar
18
revised Why is Proj of any graded ring isomorphic to Proj of a graded ring generated in degree one?
added dollars in formuale.
Feb
23
comment Rational or elliptic curves on Calabi-Yau threefolds
@LiYutong, this is because trivial canonical class implies existence of Ricci flat Kähler metrics (this is Yau), then Kobayashi-Lübke inequalities give you that $c_2(X)\ge 0$ and you have equality if and only if the Ricci flat metric is indeed flat itself. Now you conclude by the classical Bieberbach theorem.
Nov
13
awarded  Enlightened
Nov
13
awarded  Nice Answer
Oct
7
awarded  Yearling