Journal of the Ramanujan Mathematical Society

Volume 40, Issue 4, December 2025 pp. 455–460.

Some properties of finite morphisms of smooth varieties

Authors: R. V. Gurjar
Author institution:Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India.

Summary: We will prove that for a finite morphism of complex manifolds W → V if the inverse image of a closed subvariety S of V is smooth in W then S is smooth. A weaker form of Shephard-Todd, Chevalley theorem is proved. A result about totally ramified primes is proved.

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