Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics

Author:

Aida Maraj, Arpan Pal

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Statistics Theory (math.ST)

journal:

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date:

2023-09-18 16:00:00

Abstract

The motivation for this paper is to detect when an irreducible projective variety V is not toric. We do this by analyzing a Lie group and a Lie algebra associated to V. If the dimension of V is strictly less than the dimension of the above mentioned objects, then V is not a toric variety. We provide an algorithm to compute the Lie algebra of an irreducible variety and use it to provide examples of non-toric statistical models in algebraic statistics.