# Higher syzygies on surfaces with numerically trivial canonical bundle

## TL;DR

This paper characterizes property (N_p) for polarized surfaces with trivial canonical bundle by linking it to the presence or absence of specific forbidden subvarieties, providing a geometric criterion.

## Contribution

It introduces a new geometric characterization of property (N_p) on surfaces with trivial canonical bundle based on forbidden subvarieties.

## Key findings

- Property (N_p) is characterized by the nonexistence of certain subvarieties.
- Provides a geometric criterion for property (N_p) on surfaces with trivial canonical bundle.
- Connects algebraic properties to geometric configurations.

## Abstract

We characterize property $(N_p)$ on a polarized surface $(X,L)$ with trivial canonical bundle in terms of the (non)existence of certain forbidden subvarieties of $X$.