Ballico, E. On the Gauss maps of singular projective varieties. (English) Zbl 1080.14543 J. Aust. Math. Soc. 72, No. 1, 119-130 (2002). Summary: Here we study the dimension \(\delta (m,X)\) of the general fibers of the \(m\)-Gaussian map of a singular \(n\)-dimensional variety \(X \subset {\mathbb{P}}^N\). We show that for all integers \(a,b,c,d\) with \(n \leq a < b \leq c < d \leq N-1\) and \(a + d = b + c\) we have \(\delta (a,X) + \delta (d,X) \geq \delta (b,X) + \delta (c,X)\). If \(\delta (X,N-1)\) is very large we give some classification results which extend to the singular case some results of L. Ein [Invent. Math. 86, 63–74 (1986; Zbl 0603.14025)]. Cited in 1 Document MSC: 14N05 Projective techniques in algebraic geometry 14M15 Grassmannians, Schubert varieties, flag manifolds 14B05 Singularities in algebraic geometry Citations:Zbl 0603.14025 PDFBibTeX XMLCite \textit{E. Ballico}, J. Aust. Math. Soc. 72, No. 1, 119--130 (2002; Zbl 1080.14543) Full Text: DOI References: [1] Fujita, Nagoya Math. J. 115 pp 105– (1989) · Zbl 0699.14002 · doi:10.1017/S0027763000001562 [2] DOI: 10.1007/BF01391495 · Zbl 0603.14025 · doi:10.1007/BF01391495 [3] DOI: 10.1215/S0012-7094-85-05247-0 · Zbl 0603.14026 · doi:10.1215/S0012-7094-85-05247-0 [4] Beltrametti, The adjunction theory of complex projective varieties (1995) · Zbl 0845.14003 · doi:10.1515/9783110871746 [5] Zak, Tangents and secants of algebraic varieties 127 (1983) · Zbl 0795.14018 [6] Tango, J. Math. Kyoto Univ. 16 pp 201– (1976) [7] Gelfand, Discriminants, resultants and multidimensional determinants (1994) · doi:10.1007/978-0-8176-4771-1 [8] Kleiman, Enumerative Algebraic Geometry, Proc. Zeuthen Symposium 123 pp 149– (1991) · doi:10.1090/conm/123/1143552 [9] Kleiman, Proc. 1984 Vancouver Conference in Algebraic Geometry 6 (1986) [10] DOI: 10.1007/BF01444633 · Zbl 0734.14017 · doi:10.1007/BF01444633 [11] Kleiman, Real and Complex Singularities, Oslo pp 297– (1976) [12] Jouanolou, Théorémes de Bertini et applications 42 (1983) [13] Hefez, Geometry today 60 pp 143– (1985) [14] Tango, J. Math. Kyoto Univ. 14 pp 415– (1974) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.