Regularity of semi-calibrateed integral $2$-cycles

Regularity of semi-calibrateed integral $2$-cycles

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Costante Bellettini, Cambridge University
Fine Hall 314

Semi-calibrated currents naturally appear when dealing with several geometric questions, some aspects of which require a deep understanding of regularity properties of semi-calibrated currents. We will focus on the case of dimension $2$, where it turns out that semi-calibrated cycles are actually pseudo holomorphic. By using an analysis implementation of the algebro-geometric blowing up of a point we study the regularity of semi-calibrated $2$-cycles from the point of view of uniqueness of tangent cones and of local smoothness.