Boundedness of $(\epsilon, n)$-Complements for Surfaces

TL;DR

This paper proves the existence of specific types of complements for surface pairs with boundary coefficients in a DCC set, advancing the understanding of boundedness in algebraic geometry.

Contribution

It establishes the existence of $( ext{epsilon}, n)$-complements for surface pairs with boundary coefficients in a DCC set, a new result in the theory of complements.

Findings

Existence of $( ext{epsilon}, n)$-complements for surface pairs

Boundedness results for boundary coefficients in a DCC set

Advancement in the theory of complements for algebraic surfaces

Abstract

We show the existence of $(\epsilon,n)$-complements for $(\epsilon,\mathbb{R})$-complementary surface pairs when the coefficients of boundaries belong to a DCC set.