论文标题
关于格里菲斯关于Chern-Weil形式积极性的猜想的注释
A note on Griffiths' conjecture about the positivity of Chern-Weil forms
论文作者
论文摘要
让$（e，h）$为Griffiths半阳性Hermitian Holomorphic vector Bundle，等级$ 3 $比复杂的歧管$ 3 $。 In this paper, we prove the positivity of the characteristic differential form $ c_1(E,h) \wedge c_2(E,h) - c_3(E,h) $, thus providing a new evidence towards a conjecture by Griffiths about the positivity of the Schur polynomials in the Chern forms of Griffiths semipositive vector bundles.结果，我们在Chern形式之间建立了新的不平等链。此外，我们指出了如何在任何等级中获得第二个Chern表格$ C_2（E，H）$的积极性，如果$（e，h）$只是Griffiths的排名$ 2 $，则从众所周知的形式的阳性开始。本文的最后一部分概述了格里菲斯（Griffiths）猜想的最新状态，收集了几句话和开放问题。
Let $ (E,h) $ be a Griffiths semipositive Hermitian holomorphic vector bundle of rank $ 3 $ over a complex manifold. In this paper, we prove the positivity of the characteristic differential form $ c_1(E,h) \wedge c_2(E,h) - c_3(E,h) $, thus providing a new evidence towards a conjecture by Griffiths about the positivity of the Schur polynomials in the Chern forms of Griffiths semipositive vector bundles. As a consequence, we establish a new chain of inequalities between Chern forms. Moreover, we point out how to obtain the positivity of the second Chern form $ c_2(E,h) $ in any rank, starting from the well-known positivity of such form if $ (E,h) $ is just Griffiths positive of rank $ 2 $. The final part of the paper gives an overview on the state of the art of Griffiths' conjecture, collecting several remarks and open questions.
