On a theorem of Campana and Păun

Abstract

Let $X$ be a smooth projective variety over the complex numbers, and $\Delta \subseteq X$ a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and Păun: If some tensor power of the bundle ${\Omega }_X^1(\log \Delta )$ contains a subsheaf with big determinant, then $(X,\Delta )$ is of log general type. This result is a key step in the recent proof of Viehweg's hyperbolicity conjecture.

9 pages. Formatted using epigamath.sty

References in corpus (1)

• Generic positivity and applications to hyperbolicity of moduli spaces

Cited by in corpus (1)

• The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties