Minimal Terracini Loci in a Plane and Their Generalizations

被引：0

作者：

Ballico, Edoardo ^{[1
]}

机构：

[1] Univ Trento, Dept Math, I-38123 Trento, Italy

来源：

APPLIEDMATH | 2024年 / 4卷 / 02期

关键词：

projective plane; Terracini locus; double points; Veronese embedding; zero-dimensional scheme; Hilbert function; SECANT VARIETIES; VERONESE VARIETIES; HORACE METHOD; INTERPOLATION; CURVES; POINTS; RANK;

D O I：

10.3390/appliedmath4020028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study properties of the minimal Terracini loci, i.e., families of certain zero-dimensional schemes, in a projective plane. Among the new results here are: a maximality theorem and the existence of arbitrarily large gaps or non-gaps for the integers x for which the minimal Terracini locus in degree d is non-empty. We study similar theorems for the critical schemes of the minimal Terracini sets. This part is framed in a more general framework.

引用

页码：529 / 543

页数：15

共 40 条

[1] Abo H, 2009, T AM MATH SOC, V361, P767
[2] On the dimensions of secant varieties of Segre-Veronese varieties
Abo, Hirotachi
Brambilla, Maria Chiara
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2013, 192 (01) : 61 - 92
[3] New examples of defective secant varieties of Segre-Veronese varieties
Abo, Hirotachi
Brambilla, Maria Chiara
[J]. COLLECTANEA MATHEMATICA, 2012, 63 (03) : 287 - 297
[4] On non-defectivity of certain Segre-Veronese varieties
Abo, Hirotachi
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 2010, 45 (12) : 1254 - 1269
[5] Secant Varieties of Segre-Veronese Varieties Pm x Pn Embedded by O (1,2)
Abo, Hirotachi
Brambilla, Maria Chlara
[J]. EXPERIMENTAL MATHEMATICS, 2009, 18 (03) : 369 - 384
[6] JOINS AND HIGHER SECANT VARIETIES
ADLANDSVIK, B
[J]. MATHEMATICA SCANDINAVICA, 1987, 61 (02) : 213 - 222
[7] HORACE METHOD - APPLICATION TO 4TH-DEGREE INTERPOLATION
ALEXANDER, J
HIRSCHOWITZ, A
[J]. INVENTIONES MATHEMATICAE, 1992, 107 (03) : 585 - 602
[8] Alexander J., 1992, J ALGEBR GEOM, V1, P411
[9] Alexander J., 1995, J ALGEBRAIC GEOM, V4, P201, DOI [/10.1007/978-1-4615-1791-7_9, DOI 10.1007/978-1-4615-1791-7_9]
[10] ARBARELLO E, 1983, ANN SCI ECOLE NORM S, V16, P467

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