TerraciniLoci -- package for computing Terracini loci

Description

This package implements the algorithms from Section 8 of the paper Geometry of first nonempty Terracini loci by F. Galuppi, P. Santarsiero, D. Torrance, and E. Turatti.

The Terracini locus of projective variety $X$ is a subvariety of the symmetric power $X^{(r)}$ containing the closure of all sets $\{p_1,\ldots,p_r\}$ of smooth points in $X$ for which the space $\langle T_{p_1}X,\ldots,T_{p_r}X\rangle$ has less than the expected dimension.

This package exports one method, terraciniLocus, for computing the ideals of these varieties.

Authors

Version

This documentation describes version 0.5 of TerraciniLoci, released February 10, 2026.

Citation

If you have used this package in your research, please cite it as follows:

@article {MR5026390,
    AUTHOR = {Galuppi, Francesco and Santarsiero, Pierpaola and Torrance,
              Douglas A. and Turatti, Ettore Teixeira},
     TITLE = {Geometry of first nonempty {T}erracini loci},
   JOURNAL = {Commun. Contemp. Math.},
  FJOURNAL = {Communications in Contemporary Mathematics},
    VOLUME = {28},
      YEAR = {2026},
    NUMBER = {4},
     PAGES = {Paper No. 2550053},
      ISSN = {0219-1997,1793-6683},
   MRCLASS = {14J45 (14Q15 15A69)},
  MRNUMBER = {5026390},
       DOI = {10.1142/S0219199725500531},
       URL = {https://doi.org/10.1142/S0219199725500531},
}

Exports

Functions and commands
- terraciniLocus -- compute the Terracini locus of a projective variety
Methods
- terraciniLocus(ZZ,Ideal) -- see terraciniLocus -- compute the Terracini locus of a projective variety
- terraciniLocus(ZZ,Matrix,Ideal) -- see terraciniLocus -- compute the Terracini locus of a projective variety
- terraciniLocus(ZZ,RingMap) -- see terraciniLocus -- compute the Terracini locus of a projective variety

For the programmer

The object TerraciniLoci is a package, defined in TerraciniLoci.m2.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/TerraciniLoci.m2:163:0.