Examples of factorial threefolds complete intersection in $${\mathbb{P}^5}$$ with many singularities |
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Authors: | Pietro Sabatino |
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Institution: | 1.Rome,Italy |
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Abstract: | Denote by ν
m
(d) the maximal integer for which there exists for d >> 0{d \gg 0} a threefold
X ì \mathbbP5{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, nm(d) 3 j(d){\nu_m(d)\ge \varphi(d)} where j(d) ~ d5{\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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Keywords: | |
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