Monica Idà

Computing symmetric rank for symmetric tensors

We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for 2x...x2 tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetric rank strata for some secant varieties of Veronese varieties.

Betti numbers for fat point ideals in the plane: a geometric approach

We consider the open problem of determining the graded Betti numbers for fat point subschemes Z supported at general points of P 2 . We relate this problem to the open geometric problem of determining the splitting type of the pullback of P2 to the normalization of certain rational plane curves. We give a conjecture for the graded Betti numbers which would determine them in all degrees but one for every fat point subscheme supported at general points of P 2 . We also prove our Betti number conjecture in a broad range of cases. An appendix discusses many more cases in which our conjecture has been verified computationally and provides a new and more efficient computational approach for computing graded Betti numbers in certain degrees. It also demonstrates how to derive explicit conjectural values for the Betti numbers and how to compute splitting types.

Singularities of plane rational curves via projections

We consider the parameterization

A note on plane rational curves and the associated Poncelet surfaces

{\mathbf{f}}=(f_0,f_1,f_2)

Visual Impact and Mathematical Learning

of a plane rational curve

A rigidity theorem for homogeneous rational manifolds of rank 1

C

On the homogeneous ideal of the generic union of lines in ...3.ö

of degree

The Minimal Free Resolution for the First Infinitesimal Neighborhoods of n General Points in the Plane

n

Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties

, and we want to study the singularities of

Secant varieties to osculating varieties of Veronese embeddings of P^n

C