On C-fibrations over projective curves

TL;DR

This paper introduces a modified ML invariant called GML that accounts for rulings over projective bases, enabling better stratification of smooth affine rational surfaces and applications to threefolds.

Contribution

It presents the GML invariant, a new version of ML invariant that incorporates rulings over projective bases and demonstrates its computation on complex surfaces and threefolds.

Findings

GML invariant effectively stratifies smooth affine rational surfaces.

GML invariant can be computed for surfaces with no C-actions.

Application of GML to threefolds extends ML invariant analysis.

Abstract

The goal of this paper is to present a modified version (GML) of ML invariant which should take into account rulings over a projective base and allow further stratification of smooth affine rational surfaces. We provide a non-trivial example where GML invariant is computed for a smooth affine rational surface admitting no C-actions. We apply GML invariant to computation of ML invariant of some threefolds.