In this paper we prove that a nodal hypersurface in P4 with positive defect has at least (d- 1) 2 nodes, and if it has at most 2 (d- 2) (d- 1) nodes and d≥ 7 then it contains either a plane or a quadric surface. Furthermore, we prove that a nodal double cover of P3 ramified along a surface of degree 2d with positive defect has at least d(2 d- 1) nodes. We construct the largest dimensional family of nodal degree d hypersurfaces in P2n+2 with positive defect for d sufficiently large.
Maximal families of nodal varieties with defect
remke kloosterman
2022
Abstract
In this paper we prove that a nodal hypersurface in P4 with positive defect has at least (d- 1) 2 nodes, and if it has at most 2 (d- 2) (d- 1) nodes and d≥ 7 then it contains either a plane or a quadric surface. Furthermore, we prove that a nodal double cover of P3 ramified along a surface of degree 2d with positive defect has at least d(2 d- 1) nodes. We construct the largest dimensional family of nodal degree d hypersurfaces in P2n+2 with positive defect for d sufficiently large.
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