47 citations · 126 across the 12 of their papers we have counts for
19 papers
Obstructions to the ampleness of invariant jet differentials on complete intersections
Simone Diverio
We introduce the analogue, for invariant jet differentials, of the principal symbol of a differential operator: the component of maximal degree in the highest derivative. The top s…
Weakly Kähler hyperbolic manifolds and the Green--Griffiths--Lang conjecture
Francesco Bei, Simone Diverio, Philippe Eyssidieux +1
We introduce the notion of weakly Kähler hyperbolic manifold which generalizes that of Kähler hyperbolic manifold given in the early '90s by M. Gromov, and establish its basic feat…
Kobayashi hyperbolicity, negativity of the curvature and positivity of the canonical bundle
Simone Diverio
This survey article mainly addresses to graduate students and young researchers in complex geometry willing to enter the beautiful word of connections between curvature and Kobayas…
Pointwise Universal Gysin formulae and Applications towards Griffiths' conjecture
Simone Diverio, Filippo Fagioli
Let be a complex manifold, be a rank holomorphic hermitian vector bundle, and be a sequence of dimensions . Let …
On subvarieties of singular quotients of bounded domains
Benoît Cadorel, Simone Diverio, Henri Guenancia
Let be a quotient of a bounded domain in . Under suitable assumptions, we prove that every subvariety of not included in the branch locus of the quotient map i…
A note on Lang's conjecture for quotients of bounded domains
Sébastien Boucksom, Simone Diverio
It was conjectured by Lang that a complex projective manifold is Kobayashi hyperbolic if and only if it is of general type together with all of its subvarieties. We verify this con…
Rational curves on fibered Calabi-Yau manifolds
Simone Diverio, Claudio Fontanari, Diletta Martinelli
We show that a smooth projective complex manifold of dimension greater than two endowed with an elliptic fiber space structure and with finite fundamental group always contains a r…
Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle
Simone Diverio, Stefano Trapani
We show that if a compact complex manifold admits a Kähler metric whose holomorphic sectional curvature is everywhere non positive and strictly negative in at least one point, then…
Segre forms and Kobayashi-Lübke inequality
Simone Diverio
Starting from the description of Segre forms as direct images of (powers of) the first Chern form of the (anti)tautological line bundle on the projectivized bundle of a holomorphic…
About the hyperbolicity of complete intersections
Simone Diverio
This note is an extended version of a thirty minutes talk given at the "XIX Congresso dell'Unione Matematica Italiana", held in Bologna from September 12th to September 17th, 2011.…
Rational curves on Calabi-Yau threefolds and a conjecture of Oguiso
Simone Diverio
This short note is an extended abstract of a talk given at the conference "Komplexe Analysis" at the Mathematisches Forschungsinstitut Oberwolfach in September 2012. We explained s…
The exceptional set and the Green-Griffiths locus do not always coincide
Simone Diverio, Erwan Rousseau
We give a very simple criterion in order to ensure that the Green-Griffiths locus of a projective manifold is the whole manifold. Next, we use it to show that the Green-Griffiths l…
A survey on hyperbolicity of projective hypersurfaces
Simone Diverio, Erwan Rousseau
These are lecture notes of a course held at IMPA, Rio de Janiero, in september 2010: the purpose was to present recent results on Kobayashi hyperbolicity in complex geometry. Our u…
On a conjecture of Oguiso about rational curves on Calabi-Yau threefolds
Simone Diverio, Andrea Ferretti
Let X be a Calabi-Yau threefold. We show that if there exists on X a non-zero nef non-ample divisor then X contains a rational curve, provided its second Betti number is greater th…
A remark on the codimension of the Green-Griffiths locus of generic projective hypersurfaces of high degree
Simone Diverio, Stefano Trapani
We show that for every smooth generic projective hypersurface , there exists a proper subvariety such that …
Effective algebraic degeneracy
Simone Diverio, Joel Merker, Erwan Rousseau
We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2)…
Smooth metrics on jet bundles and applications
Simone Diverio
Following a suggestion made by J.-P. Demailly, for each , we endow, by an induction process, the -th (anti)tautological line bundle of an arbitrary…
Existence of global invariant jet differentials on projective hypersurfaces of high degree
Simone Diverio
Let be a smooth complex projective hypersurface. In this paper we show that, if the degree of is large enough, then there exist global sections of the…
Differential Equations on Complex Projective Hypersurfaces of Low Dimension
Simone Diverio
Let and let be a smooth complex projective hypersurface of . In this paper we find an effective lower bound for the degree of , such that every…