Tangent cones at infinity
Abstract
Abstract Let $$X\subset \mathbb {C}^m$$ X ⊂ C m be an unbounded pure k -dimensional algebraic set. We define the tangent cones $$C_{4, \infty }(X)$$ C 4 , ∞ ( X ) and $$C_{5,\infty }(X)$$ C 5 , ∞ ( X ) of X at infinity. We establish some of their properties and relations. We prove that X must be an affine linear subspace of $$\mathbb {C}^m$$ C m provided that $$C_{5, \infty }(X)$$ C 5 , ∞ ( X ) has pure dimension k . We also study the relationship between the tangent cones at infinity and representations of X outside a compact set as a branched covering.
Fields of Study & Subjects
Advanced Materials and Mechanics
Publication details
- Journal / source
- São Paulo Journal of Mathematical Sciences
- Volume
- 20
- Issue
- 2
- Publication date
- 21 September 2026
- Language
- EN