GAGA theorem for quasihomogeneous singularities

In 1956, J.-P. Serre published the famous paper “Géométrie algébrique et géométrie analytique”, showing that most complex analytic objects (such as subvarieties, meromorphic functions, coherent sheaves), if defined on algebraic varieties, arise from their counterparts which are defined algebraically. Now this result is known as GAGA theorem. A complex variety is called quasi-homogeneous if it is equipped with an invertible complex analytic contraction. I will show that this contraction defines a canonical algebraic structure on this variety, bringing on the rest of the GAGA framework. This is a joint work with Liviu Ornea.