# Smooth, nonsymplectic embeddings of rational balls in the complex projective plane

## TL;DR

This paper constructs an infinite family of smooth embeddings of rational homology balls into the complex projective plane that are not symplectic, introducing new obstructions based on Donaldson's theorem.

## Contribution

It presents the first examples of smooth but nonsymplectic embeddings of rational balls in the complex projective plane and develops a novel lattice embedding obstruction.

## Key findings

- Existence of infinitely many smooth, nonsymplectic embeddings
- New lattice embedding obstruction derived from Donaldson's theorem
- Prohibition of disjoint embeddings of the constructed examples

## Abstract

We exhibit an infinite family of rational homology balls which embed smoothly but not symplectically in the complex projective plane. We also obtain a new lattice embedding obstruction from Donaldson's diagonalisation theorem, and use this to show that no two of our examples may be embedded disjointly.