2
$\begingroup$

Let $(X, L)$ and $(Y, M)$ be two polarized abelian varieties .

According to Birkenhake C. and Lange H. in Complex Abelian Varieties a homomorphism of polarized abelian varieties $f:(Y, M)\longrightarrow (X, L)$ is a homomorphism of complex tori $f:Y\longrightarrow X$ such that $f^{*}c_1(L) = c_1(M)$.

Question: It's true that $f^*c_1(L)=c_1(f^*L)$?

$\endgroup$

1 Answer 1

1
$\begingroup$

Yes! This is sometime called naturality of Chern classes. You can find it in many books, for instance Complex Geometry - An Introduction | Daniel Huybrechts, or Differential forms in algebraic topology by Bott and Tu.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.