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 - Funding Information:
this paper, and for many useful discussions and advice about its contents. We also thank Dano Kim and Luigi Lombardi for reading and commenting on a draft version. During the preparation of the paper, CH was partially supported by NSF grants DMS-1300750 and DMS-1265285 and by a grant from the Simons Foundation (Award #256202). MP was partially supported by NSF grant DMS-1405516 and by a Simons Fellowship. CS was partially supported by NSF grants DMS-1404947 and DMS-1551677, and by a Centennial Fellowship from the American Mathematical Society.
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 - http://www.scopus.com/inward/record.url?scp=85052214724&partnerID=8YFLogxK

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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 -