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A note on nodal determinantal hypersurfaces

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Abstract

We prove that a general determinantal hypersurface of dimension 3 is nodal. Moreover, in terms of Chern classes associated with bundle morphisms, we derive a formula for the intersection homology Euler characteristic of a general determinantal hypersurface.

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Acknowledgements

The author is greatly indebted to Prof. Chin-Lung Wang, Prof. Baosen Wu and Prof. Ching-Jui Lai for many useful discussions, and to Dr. Yinbang Lin for valuable comments. The author would like to thank the anonymous referee for comments and suggestions and Prof. I. Cheltsov for his help. The author also thanks Tsinghua University, Southeast University, Yau Mathematical Sciences Center and Shing-Tung Yau Center and School of Mathematics for providing support and a stimulating environment.

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  1. Shing-Tung Yau Center and School of Mathematics, Southeast University, Nanjing, 211189, China

    Sz-Sheng Wang

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Wang, SS. A note on nodal determinantal hypersurfaces. Geom Dedicata 208, 97–111 (2020). https://doi.org/10.1007/s10711-020-00512-y

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