Seifert $G_m$-bundles

TL;DR

This paper develops foundational results for Seifert G_m-bundles over arbitrary normal varieties, including classification and smoothness criteria, extending classical notions to a broader algebraic setting.

Contribution

It provides the first comprehensive classification and smoothness criteria for Seifert G_m-bundles over normal varieties, generalizing previous topological and holomorphic theories.

Findings

Classification of Seifert G_m-bundles over normal varieties

Smoothness criteria for these bundles

Extension of classical Seifert bundle theory to algebraic varieties

Abstract

A Seifert bundle over a variety X is a variety Y with a proper action of the multiplicative group such that the quotient is X. The topological version of this notion (using circle actions) was introduced by Seifert, the holomorphic version by Orlik and Wagreich. The aim of this paper is to provide the foundational results for Seifert bundles over an arbitrary normal variety X. The main results are a classification and a smoothness criterion.