Modular Operads of Embedded Curves

TL;DR

This paper constructs a modular operad structure for a class of embedded algebraic curves, specifically focusing on k-log-canonically embedded curves for k ≥ 5, advancing the understanding of their algebraic and geometric properties.

Contribution

It introduces a new modular operad framework for k-log-canonically embedded curves, expanding the algebraic tools available for studying these geometric objects.

Findings

Established a modular operad structure for k-log-canonically embedded curves.

Extended the operadic approach to a new class of algebraic curves.

Provided foundational work for future algebraic and geometric investigations.

Abstract

For each k greater than or equal to 5, we construct a modular operad of "k-log-canonically embedded" curves.