Noether–Lefschetz theory with base locus
Copyright policy )Noether–Lefschetz theory with base locus
Let $Z$ be a closed subscheme of a smooth complex projective variety $Y\subseteq \Ps^N$, with $\dim\,Y=2r+1\geq 3$. We describe the intermediate N��ron-Severi group (i.e. the image of the cycle map $A_r(X)\to H_{2r}(X;\mathbb{Z})$) of a general smooth hypersurface $X\subset Y$ of sufficiently large degree containing $Z$.
18 pages, Added references
Topological properties in algebraic geometry, Noether–Lefschetz theory, Néron-Severi group, Settore MAT/03 - GEOMETRIA, Picard groups, Néron-Severi group, Noether-Lefschetz theory, Blowing-up; Borel-Moore homology; Isolated singularities; Monodromy representation; Néron-Severi group; Noether-Lefschetz theory; Mathematics (all), Algebraic cycles, 14B05, 14C20, 14C21, 14C22, 14C25, 14C30, 14F43, 14F45, 14J70, Mathematics - Algebraic Geometry, Noether–Lefschetz theory ; Néron–Severi group ; Borel–Moore homology ; Monodromy representation ; Isolated singularities ; Blowing-up, Transcendental methods, Hodge theory (algebro-geometric aspects), FOS: Mathematics, Mathematics (all), Hypersurfaces and algebraic geometry, Borel–Moore homology, Borel-Moore homology, Néron–Severi group, Blowing-up, Monodromy representation, Algebraic Geometry (math.AG), Isolated singularities
Topological properties in algebraic geometry, Noether–Lefschetz theory, Néron-Severi group, Settore MAT/03 - GEOMETRIA, Picard groups, Néron-Severi group, Noether-Lefschetz theory, Blowing-up; Borel-Moore homology; Isolated singularities; Monodromy representation; Néron-Severi group; Noether-Lefschetz theory; Mathematics (all), Algebraic cycles, 14B05, 14C20, 14C21, 14C22, 14C25, 14C30, 14F43, 14F45, 14J70, Mathematics - Algebraic Geometry, Noether–Lefschetz theory ; Néron–Severi group ; Borel–Moore homology ; Monodromy representation ; Isolated singularities ; Blowing-up, Transcendental methods, Hodge theory (algebro-geometric aspects), FOS: Mathematics, Mathematics (all), Hypersurfaces and algebraic geometry, Borel–Moore homology, Borel-Moore homology, Néron–Severi group, Blowing-up, Monodromy representation, Algebraic Geometry (math.AG), Isolated singularities
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