47 citations · 126 across the 12 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…
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…
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)…
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…