We study analytic deformations of holomorphic foliations given by homogeneous integrable one-forms in the complex affine space ${\mathbb{C}}^n$. The deformation is supposed to be of first order (order one in the parameter). We also assume that the deformation is given by homogeneous polynomial one-forms. The deformation takes place in the affine space since we are not assuming that the foliations descent to the projective space. We describe the space of such deformations in three main situations: (1) the foliation is given by the level hypersurfaces of a homogeneous polynomial. (2) the foliation is rational, i.e., has a first integral of type $P^r/Q^s$ for some homogeneous polynomials $P,Q$. (3) the foliation is logarithmic of a generic type. We prove that, for each class mentioned above, the first order homogeneous deformations of same degree are in the very same class. We also investigate the existence of such deformations with different degrees.

我们研究由复仿射空间中的均一可积一形式给出的全同叶的解析变形 ${\mathbb{C}}^{ñ}$。变形应该是一阶的（参数中的一阶）。我们还假设变形是由齐次多项式一形式给出的。变形发生在仿射空间中，因为我们没有假设叶面下降到射影空间。我们在以下三种主要情况下描述了这种变形的空间：（1）叶面是由齐次多项式的水平超曲面给出的。（2）叶面是有理的，即具有第一类型的整数$P^{\mathrm{[R}}/{问}^s$ 对于一些齐次多项式 $P，问$。（3）叶是泛型的对数。我们证明，对于上述每个类，相同程度的一阶均匀变形都在同一类中。我们还研究了这种程度不同的变形的存在。