---
abstract: 'In this work we study neighborhoods of curves in surfaces with positive self-intersection that can be embeeded as a germ of neighborhood of a curve on the projective plane.'
author:
- 'M. Falla Luza'
- 'P. Sad'
title: Positive Neighborhoods of Curves
---

Introduction
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We study in this paper neighborhoods of compact, smooth, holomorphic curves of complex surfaces which have positive self intersection number. Our main purpuse is to give a condition that guarantees the existence of an embedding of a neighborhood of the curve into the projective plane. The first example of a result on this problem comes from [@FA]; in that paper the authors showed that if the curve has genus 0 and self intersection number equal to 1 then the existence of three different fibrations over it implies that some neighborhood is diffeomorphic to a neighborhood of the line in the projective plane. In this paper we consider curves of self-intersection $d^2$ with $d \geq 2$.

Since a fibration over a curve of genus 0 is defined by a local submersion over $\Pp^1$ (that is, defined in a neighborhood of the curve), we may wonder if in the case of higher genus the existence 