On rank 3 quadratic equations of Veronese embeddings

Key Points

• The study reveals the geometric structure of the locus of rank 3 quadratic equations, analyzing their properties.
• Key findings include the exploration of the minimal irreducible decomposition of these equations and their desingularizations.
• Important insights were gained regarding the non-singularity and singularity of the irreducible components of the Veronese variety.
• The geometric properties explored have implications for understanding the structure of quadratic equations in algebraic geometry.