Euler-Chow series for scrolls and ruled surfaces

TL;DR

This paper proves that the Euler-Chow series for ruled surfaces and scrolls is rational through explicit computation, advancing understanding of their algebraic and geometric properties.

Contribution

It provides the first explicit proof of the rationality of Euler-Chow series for these classes of algebraic surfaces.

Findings

Euler-Chow series for ruled surfaces is rational

Explicit computation method demonstrated

Enhances understanding of algebraic surface invariants

Abstract

We prove that the Euler-Chow series for ruled surfaces and scrolls is rational by means of an explicit computation.