VARIETIES WITH ONE APPARENT DOUBLE POINT

By C. Ciliberto, Massimiliano Mella, Francesco G. Russo. 2002

63 citations recorded by the source corpus.

The number of apparent double points of a smooth, irreducible projective variety X of dimension n in P 2n+1 is the number of secant lines to X passing through the general point of P 2n+1 . This classical notion dates back to Severi. In the present paper we classify smooth varieties of dimension at most three having one apparent double point. The techniques developed for this purpose allow us to treat a wider class of projective varieties.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cd9ce423731c07caa3bd4443797688908b64b341

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In Computational Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

On the Concept of k‐Secant Order of a Variety (2006, methodology): “Here, together with some monodromy argument, we use the so-called technique of degeneration of projections introduced in [6] and [7] to show that the (k+1)-contact loci consist of (k+1)-tuples of lines, so that the surface is a scroll.”
Varieties with minimal secant degree and linear systems of maximal dimension on surfaces (2004, methodology): “7), where we exploit and generalize the technique, introduced in [18], of degeneration of projections, based on a beautiful idea of Franchetta (see [26,27]).”
Varieties with quadratic entry locus, I (2007, methodology): “ δ-codimensional subspace of TxX passing through xis birational, then X is an LQEL-manifold of type δ. (iii) If X⊂ PN is an LQEL-manifold of typeδ>0, then Xis rational. We recall some results from [CMR] (see also [CR]) in order to point out a relation between the entry loci of a variety and a gen”
Classical Algebraic Geometry: A Modern View (2012, methodology): “We refer to [102] for more information about OADP subvarieties.”
Legendrian varieties (2004, background): “and were extensively studied in [23, 7, 17]; see also [6] since they are nice examples of varieties with one apparent double point.”
Singularities of linear systems and the Waring problem (2004, methodology): “In doing this I show the rationality of varieties with one apparent (k + 1)-tuple secant Pk, improving on results of [ CMR ], see also [CR].”
Decomposition of homogeneous polynomials with low rank (2010, unknown): “∈ Z (see [19], [17], [18], [9] also for”