Multigraded Sylvester forms, Duality and Elimination

Abstract: This talk will report on joint work with Laurent Busé and Navid Nemati. First, the classical situation of the theory of resultants and Sylvester forms in a standard graded algebra will be presented, as it was developed by Jouanolou in a series of monographs. Then we will explain the extension of this theory to the multi-graded case (which corresponds to a product of projective spaces, in place of a single one). This builds on the previous work of two Ph.D. students of Jouanolou (Chaichaa and Chkiriba) and an extension of a duality result from the classical case to this more general setting. We will illustrate these in a very simple case, by providing a family of formulas that extends the work of Dixon.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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