Publications (8)
Degree of Rational Maps versus Syzygies
M. Chardin, S. H. Hassanzadeh, A. Simis
One proves a far-reaching upper bound for the degree of a generically finite rational map between projective varieties over a base field of arbitrary characteristic. The bound is e…
Plane Cremona maps: saturation and regularity of the base ideal
S. H. Hassanzadeh, A. Simis
One studies plane Cremona maps by focusing on the ideal theoretic and homological properties of its homogeneous base ideal ("indeterminacy locus"). The {\em leitmotiv} driving a go…
Tangent Algebras
A. Simis, B. Ulrich, W. V. Vasconcelos
\noindent We study the Zariski tangent cone $T_X\stackrelÏ{\lar} X$ to an affine variety and the closure of in . We focus on the compa…
On catalecticant perfect ideals of codimension 2
A. Simis, Z. Ramos
One deals with catalectic codimension two perfect ideals and certain degenerations thereof, with a view towards the nature of their symbolic powers. In the spirit of [10] one consi…
Bounds for the degree and Betti sequences along a graded resolution
W. A. da Silva, S. H. Hassanzadeh, A. Simis
The main goal of this paper is to size up the minimal graded free resolution of a homogeneous ideal in terms of its generating degrees. By and large, this is too ambitious an objec…
A characteristic free criterion of birationality
A. V. Dória, S. H. Hassanzadeh, A. Simis
One develops {\em ab initio} the theory of rational/birational maps over reduced, but not necessarily irreducible, projective varieties in arbitrary characteristic. A numerical inv…
Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
C. Renteria, A. Simis, R. H. Villarreal
Let K be a finite field with q elements and let X be a subset of a projective space P^{s-1}, over the field K, which is parameterized by Laurent monomials. Let I(X) be the vanishin…
On the homology of two-dimensional elimination
J. Hong, A. Simis, W. V. Vasconcelos
We study birational maps with empty base locus defined by almost complete intersection ideals. Birationality is shown to be expressed by the equality of two Chern numbers. We provi…