Abstract
In this paper, we show that the Δ-genus for any connected polarized demi-normal scheme over an algebraically closed field k. As an application, we obtain for any KSBA stable log scheme , where I is the Cartier index of . We also construct examples of KSBA stable log schemes with I = 1 and , which shows the inequality is sharp when I = 1.
Acknowledgments
We would like to express our sincere gratitude to Prof. Jinxing Cai and Prof. Wenfei Liu, for their invaluable guidance and instruction. Additionally, we would like to extend our thanks to the anonymous reviewers for their insightful comments and suggestions. Their insightful comments and suggestions have been instrumental in improving this paper.