Dagger closure and solid closure in graded dimension two

TL;DR

This paper introduces a graded version of dagger closure and demonstrates its equivalence to solid closure for homogeneous ideals in two-dimensional graded domains over a field.

Contribution

It defines a graded dagger closure and proves its coincidence with solid closure in a specific algebraic setting.

Findings

Graded dagger closure is equivalent to solid closure in the studied context.

The result applies to homogeneous ideals in two-dimensional graded domains.

Provides new insights into closure operations in algebraic geometry.

Abstract

We introduce a graded version of dagger closure and prove that it coincides with solid closure for homogeneous ideals in two dimensional $\mathbb{N}$-graded domains of finite type over a field.