Higher Genus RiemannRoch and the Geometry of Curves
Higher Genus Riemann-Roch and the Geometry of Curves Riemann-Roch theorem is elegant and its proof is a cornerstone of any first course in algebraic geometry or complex analysis (for Riemann surfaces), its implications, particularly for curves of genus $g \ge 2$, continue to drive research and provide essential tools for understanding their intricate geometry. This post aims to delve into the Riemann-Roch theorem beyond the familiar low-genus cases, exploring its quantitative power and its role in unlocking deeper properties of algebraic curves. ...