The project titled "Projective Closure of Affine Monomial Curves" aims to understand the geometric properties of the projective closure of affine monomial curves. The study will use homological and combinatorial techniques. The project is based on extensive research on numerical semigroup properties and the PI's experience in this area. Initial research on three monomial curve classes, Bresinsky, Arslan, and Backelin, revealed that common behavior among affine curves does not guarantee projective closures.
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