Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA remark on the codimension of the Green-Griffiths locus of generic projective hypersurfaces of high degree
109
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that for every smooth generic projective hypersurface $Xsubsetmathbb P^{n+1}$, there exists a proper subvariety $Ysubsetneq X$ such that $operatorname{codim}_X Yge 2$ and for every non constant holomorphic entire map $fcolonmathbb Cto X$ one has $f(mathbb C)subset Y$, provided $deg Xge 2^{n^5}$. In particular, we obtain an effective confirmation of the Kobayashi conjecture for threefolds in $mathbb P^4$.
rate research
Read More
In this note, we answer a question on the extension of $L^{2}$ holomorphic functions posed by Ohsawa.
We show that the boundary of any bounded strongly pseudoconvex complete circular domain in $mathbb C^2$ must contain points that are exceptionally tangent to a projective image of the unit sphere.
We prove that certain possibly non-smooth Hermitian metrics are Griffiths-semipositively curved if and only if they satisfy an asymptotic extension property. This result answers a question of Deng--Ning--Wang--Zhou in the affirmative.
We study the variation of linear sections of hypersurfaces in $mathbb{P}^n$. We completely classify all plane curves, necessarily singular, whose line sections do not vary maximally in moduli. In higher dimensions, we prove that the family of hyperplane sections of any smooth degree $d$ hypersurface in $mathbb{P}^n$ vary maximally for $d geq n+3$. In the process, we generalize the classical Grauert-Mulich theorem about lines in projective space, both to $k$-planes in projective space and to free rational curves on arbitrary varieties.
We prove that a certain positivity condition, considerably more general than pseudoconvexity, enables one to conclude that the regular order of contact and singular order of contact agree when these numbers are $4$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
