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arXiv · 2501.06361

Castelnuovo-Mumford Regularity over Scrolls and Splitting Criteria

F. Malaspina·G. Sankaran
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Abstract

We introduce and study a notion of Castelnuovo-Mumford regularity suitable for scrolls obtained as projectivisations of sums of line bundles on $\mathbb P^m$. We show that this is a natural generalisation of the well known regularity on projective and multiprojective spaces and we prove Horrocks-type splitting criteria for vector bundles.

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F. Malaspina, G. Sankaran. 2025-01-10. Castelnuovo-Mumford Regularity over Scrolls and Splitting Criteria. https://arxiv.org/abs/2501.06361

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