Decomposition of the Tschirnhausen module for coverings on decomposable ℙ¹-bundles

2025/09/14 by Youngook Choi, Choi, Youngook, Hristo Iliev +3
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2509.11227

Abstract

In this note, we show that for a smooth algebraic variety Y and a smooth m-section X of the ℙ¹-bundle f : ℙ(O_Y ⊕ O_Y(E)) \longrightarrow Y, where E is an effective divisor on Y satisfying H¹(Y, O_Y(kE)) = 0 for all k = 1, …, m-1, the Tschirnhausen module of the induced covering f|_X : X \longrightarrow Y is completely decomposable. We then apply it to coverings of curves arising in such a way.

Citations

• On the Tschirnhausen module of coverings of curves on decomposable ruled surfaces and applications
• Non-reduced components of the Hilbert scheme of curves using triple covers
• Vector bundles and finite covers

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