Marta Casanellas
Abstract
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We prove that if X ⊂ P N X \subset \mathbb {P}^N has dimension k k and it is r r -Buchsbaum with r > max ( codim X − k , 0 ) r>\max {(\operatorname {codim}{X}-k,0)} , then X X is contained in at most one variety of minimal degree and dimension k + 1 k+1 .
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We prove that if X ⊂ P N X \subset \mathbb {P}^N has dimension k k and it is r r -Buchsbaum with r > max ( codim X − k , 0 ) r>\max {(\operatorname {codim}{X}-k,0)} , then X X is contained in at most one variety of minimal degree and dimension k + 1 k+1 .
Key concepts: Mathematics, Degree (music), Dimension (graph theory), Uniqueness, Variety (cybernetics), Combinatorics, Scheme (mathematics), Discrete mathematics