TY - CHAP
T1 - Algebraic fiber spaces over abelian varieties
T2 - Around a recent theorem by Cao and Păun
AU - Hacon, Christopher
AU - Popa, Mihnea
AU - Schnell, Christian
N1 - Publisher Copyright:
© 2018 American Mathematical Society.
PY - 2018
Y1 - 2018
N2 - We present a simplified proof for a recent theorem by Junyan Cao and Mihai Păun, confirming a special case of Iitaka’s Cn,m conjecture: if f X → Y is an algebraic fiber space, and if the Albanese mapping of Y is generically finite over its image, then we have the inequality of Kodaira dimensions κ(X) ≥ κ(Y) + κ(F), where F denotes a general fiber of f. We include a detailed survey of the main algebraic and analytic techniques, especially the construction of singular hermitian metrics on pushforwards of adjoint bundles (due to Berndtsson, Păun, and Takayama).
AB - We present a simplified proof for a recent theorem by Junyan Cao and Mihai Păun, confirming a special case of Iitaka’s Cn,m conjecture: if f X → Y is an algebraic fiber space, and if the Albanese mapping of Y is generically finite over its image, then we have the inequality of Kodaira dimensions κ(X) ≥ κ(Y) + κ(F), where F denotes a general fiber of f. We include a detailed survey of the main algebraic and analytic techniques, especially the construction of singular hermitian metrics on pushforwards of adjoint bundles (due to Berndtsson, Păun, and Takayama).
UR - https://www.scopus.com/pages/publications/85052214724
U2 - 10.1090/conm/712/14346
DO - 10.1090/conm/712/14346
M3 - Chapter
AN - SCOPUS:85052214724
T3 - Contemporary Mathematics
SP - 143
EP - 195
BT - Contemporary Mathematics
PB - American Mathematical Society
ER -