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math.AC2020
Waring problems and the Lefschetz properties
Thiago Dias, Rodrigo Gondim
We study three variations of the Waring problem for polynomials, concerning the Waring rank, the border rank and the cactus rank of a form and we show how the Lefschetz properties…
math.AC2018
The Jordan type of graded Artinian Gorenstein algebras
Barbara Costa, Rodrigo Gondim
We study the general Jordan type of standard graded Artinian Gorenstein algebras, it is a finer invariant than Weak and Strong Lefschetz properties for those algebras. We prove tha…
math.AC2018
On mixed Hessians and the Lefschetz properties
Rodrigo Gondim, Giuseppe Zappala'
We introduce a new type of Hessian matrix, that we call Mixed Hessian. The mixed Hessian is used to compute the rank of a multiplication map by a power of a linear form in a standa…