Here is my question which is a classical result:

Let $f:X\to Z$ be a surjective smooth morphism between smooth projective varieties over an algebraically closed field $k$ of characteristic zero. Let $\dim Z > 0$, then why $-K_{X/Z}$ is not ample?

In paper [KMM92] Rational connectedness and boundedness of Fano manifolds due to János Kollár, Yoichi Miyaoka and Shigefumi Mori, they state this as a corollary (Corollary 2.8) without proof. In this case $K_X=f^*K_Z+K_{X/Z}$. In [KMM92] they claim that this result can be showed by bend-and-break technique as in Theorem 2.1, but I don't know why? Actually I have no idea how to use bend-and-break technique here???

Thank you for your help!

Here is my question which is a classical result:

Let $f:X\to Z$ be a surjective smooth morphism between smooth projective varieties over an algebraically closed field $k$ of characteristic zero. Let $\dim Z > 0$, then why $-K_{X/Z}$ can not be ample?

In paper [KMM92] Rational connectedness and boundedness of Fano manifolds due to János Kollár, Yoichi Miyaoka and Shigefumi Mori, they state this as a corollary (Corollary 2.8) without proof. In this case $K_X=f^*K_Z+K_{X/Z}$. In [KMM92] they claim that this result can be showed by bend-and-break technique as in Theorem 2.1, but I don't know why? Actually I have no idea how to use bend-and-break technique here???

Thank you for your help!

Here is my question which is a classical result:

Let $f:X\to Z$ be a surjective smooth morphism between smooth projective varieties over an algebraically closed field $k$ of characteristic zero. Let $\dim Z > 0$, then why $K_{X/Z}$ is not ample?

In paper [KMM92] Rational connectedness and boundedness of Fano manifolds due to János Kollár, Yoichi Miyaoka and Shigefumi Mori, they state this as a corollary (Corollary 2.8) without proof. In this case $K_X=f^*K_Z+K_{X/Z}$. In [KMM92] they claim that this result can be showed by bend-and-break technique as in Theorem 2.1, but I don't know why? Actually I have no idea how to use bend-and-break technique here???

Thank you for your help!

Here is my question which is a classical result:

Let $f:X\to Z$ be a surjective smooth morphism between smooth projective varieties over an algebraically closed field $k$ of characteristic zero. Let $\dim Z > 0$, then why $-K_{X/Z}$ is not ample?

In paper [KMM92] Rational connectedness and boundedness of Fano manifolds due to János Kollár, Yoichi Miyaoka and Shigefumi Mori, they state this as a corollary (Corollary 2.8) without proof. In this case $K_X=f^*K_Z+K_{X/Z}$. In [KMM92] they claim that this result can be showed by bend-and-break technique as in Theorem 2.1, but I don't know why? Actually I have no idea how to use bend-and-break technique here???

Thank you for your help!

Here is my question which is a classical result:

Let $f:X\to Z$ be a surjective smooth morphism between smooth projective varieties over an algebraically closed field $k$ of characteristic zero. Let $\dim Z > 0$, then why $K_{X/Z}$ is not ample?

In paper [KMM92] Rational connectedness and boundedness of Fano manifolds due to János Kollár, Yoichi Miyaoka and Shigefumi Mori, they state this as a corollary (Corollary 2.8) without proof. In this case $K_X=f^*K_Z+K_{X/Z}$. In [KMM92] they claim that this result can be showed by bend-and-break technique as in Theorem 2.1, but I don't know why? Actually I have no idea how to use bend-and-break technique here???

Thank you for your help!

Here is my question which is a classical result:

Let $f:X\to Z$ be a surjective smooth morphism between smooth projective varieties over an algebraically closed field $k$ of characteristic zero. Let $\dim Z > 0$, then why $K_{X/Z}$ is not ample?

In paper [KMM92] Rational connectedness and boundedness of Fano manifolds due to János Kollár, Yoichi Miyaoka and Shigefumi Mori, they state this as a corollary (Corollary 2.8) without proof. In this case $K_X=f^*K_Z+K_{X/Z}$. In [KMM92] they claim that this result can be showed by bend-and-break technique as in Theorem 2.1, but I don't know why? Actually I have no idea how to use bend-and-break technique here???

Thank you for your help!