Abstract
Denote by ν m (d) the maximal integer for which there exists for \({d \gg 0}\) a threefold \({X\subset \mathbb{P}^5}\) complete intersection of hypersurfaces of degree respectively d and d − 1 such that X has only ordinary singularities of order m and |Sing(X)| = ν m (d). We prove that, \({\nu_m(d)\ge \varphi(d)}\) where \({\varphi(d)\sim d^5}\) asymptotically. This result extends (Di Gennaro and Franco in Commun Contemp Math 10(5):745–764, 2008, Corollary 2.10).
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Communicated by C. Ciliberto.
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Sabatino, P. Examples of factorial threefolds complete intersection in \({\mathbb{P}^5}\) with many singularities. Ricerche mat. 58, 285–297 (2009). https://doi.org/10.1007/s11587-009-0064-y
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DOI: https://doi.org/10.1007/s11587-009-0064-y
Keywords
- Complete intersection
- Isolated singularity
- \({\mathbb{Q}}\)-factoriality
- Nèron–Severi group
- Projective variety
- Factoriality