A generalization of Esteves--Homma's example of tangentially degenerate curves

TL;DR

This paper introduces a new method for constructing tangentially degenerate curves with birational Gauss maps, generalizing previous examples and providing a curve with a tangent line intersecting the curve at multiple points, answering an open question.

Contribution

It generalizes Esteves--Homma's example of tangentially degenerate curves and constructs a smooth curve with a tangent line intersecting at three or more points, addressing a prior open problem.

Findings

Constructed tangentially degenerate curves with birational Gauss maps.

Provided a curve with a tangent line containing three or more points.

Answered Kaji's question affirmatively.

Abstract

This paper presents a method of a construction of tangentially degenerate curves with a birational Gauss map, focusing on the non-classicality of automorphisms. This method describes a generalization of Esteves--Homma's example of this kind. In addition, this paper presents a smooth projective curve with a birational Gauss map such that a general tangent line contains three or more points of the curve, which answers a question raised by Kaji in the affirmative.