Collectanea Mathematica

, Volume 65, Issue 3, pp 303–330 | Cite as

Tangential varieties of Segre–Veronese varieties

  • Luke Oeding
  • Claudiu RaicuEmail author


We determine the minimal generators of the ideal of the tangential variety of a Segre–Veronese variety, as well as the decomposition into irreducible \({GL}\)-representations of its homogeneous coordinate ring. In the special case of a Segre variety, our results confirm a conjecture of Landsberg and Weyman.


Tangential varieties Segre varieties Veronese varieties 

Mathematics Subject Classification (1991) 

14L30 15A69 15A72 



We would like to thank J. M. Landsberg, Giorgio Ottaviani, and Bernd Sturmfels for useful suggestions, as well as the anonymous referee for many valuable comments. The Macaulay2 algebra software [10] was helpful in many experiments, particularly through the SchurRings package [18] which was used to predict some of the syzygy functors described in the paper. The second author was partially supported by the National Science Foundation Grant No. 1303042.


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Copyright information

© Universitat de Barcelona 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA
  3. 3.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  4. 4.Department of Mathematics and Statistics Auburn UniversityAuburnUSA

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