# Exotic Branes from del Pezzo Surfaces

## TL;DR

This paper explores the connection between del Pezzo surfaces and M-theory branes, proposing that higher genus curves correspond to exotic, non-geometric backgrounds and revealing new insights into brane polarization.

## Contribution

It introduces a novel interpretation of higher genus curves on del Pezzo surfaces as exotic branes in M-theory, expanding the geometric-brane correspondence.

## Key findings

- Higher genus curves relate to non-geometric backgrounds.
- Number of special directions equals the genus of the curve.
- Curve addition corresponds to brane polarization effects.

## Abstract

We revisit a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces, in which rational curves on the del Pezzo are related to ${1\over 2}$-BPS branes of the corresponding compactification. We argue that curves of higher genus correspond to non-geometric backgrounds of the M-theory compactifications, which are related to exotic branes. In particular, the number of "special directions" of the exotic brane is equal to the genus of the corresponding curve. We also point out a relation between addition of curves in the del Pezzo and the brane polarization effect.