10 citations · 10 across the 9 of their papers we have counts for
14 papers
On minimal Gorenstein Hilbert function
Lenin Bezerra, Rodrigo Gondim, Giovanna Ilardi +1
We conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing codimension and length. We prove the co…
Counting square free monomial cremona maps
Bárbara Costa, Thiago Dias, Rodrigo Gondim +1
We give a complete list of square-free Cremona maps with at most six variables, up to equivalence classes. We also build an algorithm to count monomial square-free Cremona transfor…
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…
Developable cubics in and the Lefschetz locus in
Thiago Fassarella, Viviana Ferrer, Rodrigo Gondim
We provide a classification of developable cubic hypersurfaces in . Using the correspondence between forms of degree on and Artinian Gorenstein $\mat…
Higher order Jacobians, Hessians and Milnor algebras
Alexandru Dimca, Rodrigo Gondim, Giovanna Ilardi
We introduce and study higher order Jacobian ideals, higher order and mixed Hessians, higher order polar maps, and higher order Milnor algebras associated to a reduced projective h…
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…
Lefschetz Properties for Higher Order Nagata Idealizations
Armando Cerminara, Rodrigo Gondim, Giovanna Ilardi +1
We study a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicity as a bigr…
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…
Hypersurfaces with vanishing hessian via Dual Cayley Trick
Rodrigo Gondim, Francesco Russo, Giovanni Staglianò
We present a general construction of hypersurfaces with vanishing hessian, starting from any irreducible non-degenerate variety whose dual variety is a hypersurface and based on th…
Lefschetz properties for Artinian Gorenstein algebras presented by quadrics
Rodrigo Gondim, Giuseppe Zappalà
We introduce a family of standard bigraded binomial Artinian Gorenstein algebras, whose combinatoric structure characterizes the ones presented by quadrics. These algebras provide,…
Counting Square free Cremona monomial maps
Barbara Costa, Thiago Dias, Rodrigo Gondim
We use combinatorics tools to reobtain the classification of monomial quadratic Cremona transformations in any number of variables given in \cite{SV2} and to classify and count squ…
On higher Hessians and the Lefschetz properties
Rodrigo Gondim
We deal with a generalization of a Theorem of P. Gordan and M. Noether on hypersurfaces with vanishing (first) Hessian. We prove that for any given , and $2\leq…
On a Frobenius problem for polynomials
Ricardo Conceição, Rodrigo Gondim, Miguel Rodriguez
We extend the famous diophantine Frobenius problem to the case of polynomials over a field . Similar to the classical problem, we show that the case of the Frobenius probl…
On cubic hypersurfaces with vanishing hessian
Rodrigo Gondim, Francesco Russo
If is a reduced complex hypersurface, the hessian of (or by abusing the terminology the hessian of ) is the determinant of the matrix of the s…