On the Singular Locus of a Plane Projection of a Complete Intersection

TL;DR

This paper investigates the number of self-intersections in a plane projection of a generic complete intersection curve and explores its tropical geometry counterpart.

Contribution

It provides a formula for counting self-intersections of projected curves and connects the problem to tropical geometry analysis.

Findings

Derived a formula for self-intersection count

Linked classical and tropical geometry approaches

Extended understanding of curve projections

Abstract

In this paper, we compute the number of self-intersections of a plane projection of a generic complete intersection curve defined by polynomials with the given support. Moreover, we discuss the tropical counterpart of this problem.