An "Anti-Iitaka theorem" in positive characteristic

Given a fibration f:X→Y of complex projective varieties with general fiber F, the Iitaka conjecture predicts the inequality κ(K_X)≥κ(K_F)+κ(K_Y). Recently Chang has shown that if one further assumes that the stable base locus 𝔹(−K_X) is vertical over Y, then we have a similar inequality for the anticanonical divisor κ(−K_X)≤κ(−K_F)+κ(−K_Y) . Both Iitaka's conjecture and Chang's theorem are known to fail in positive characteristic. In this talk I will explain how to recover Chang's theorem for a large class of fibrations in positive characteristic.

Note:
Refreshments at 3:30pm