1b:I[76749,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"default"] 1c:I[3486,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"default"] 1d:I[17707,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"default"] 1e:I[66528,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"default"] 1f:I[63176,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"default"] 20:I[87099,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"default"] 21:I[26200,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"Group"] 22:I[23365,["/_next/static/chunks/bf18fea59be6d5b1.js","/_next/static/chunks/1ba21a8e081e29d1.js","/_next/static/chunks/0383663887945ae7.js","/_next/static/chunks/2060b26370dc6c0a.js","/_next/static/chunks/c89b4435b8c37fcf.js","/_next/static/chunks/8ddf2550f38c2f2a.js","/_next/static/chunks/5bf36002c846d2d8.js"],"default"] 23:T49d,We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of a duality statement between the cone of pseudo-effective divisors and the cone of “movable curves”, which is obtained from a general theory of movable intersections and approximate Zariski decomposition for closed positive ( 1 , 1 ) (1,1) -currents. As a corollary, a projective manifold has a pseudo-effective canonical bundle if and only if it is not uniruled. We also prove that a 4-fold with a canonical bundle which is pseudo-effective and of numerical class zero in restriction to curves of a good covering family, has non-negative Kodaira dimension.

Mihai Păun

Publications