Horrocks splitting on Segre–Veronese varieties

We prove an analogue of Horrocks’ splitting theorem for Segre–Veronese varieties building upon the theory of Tate resolutions on products of projective spaces.

Moment Varieties of Gaussian Mixtures

The points of a moment variety are the vectors of all moments up to some order, for a givenfamily of probability distributions. We study the moment varieties for mixtures of multivariate Gaussians.Following up on Pearson's classical work from 1894, we apply current tools from computational algebrato recover the parameters from the moments. Our moment varieties extend objects familiar to algebraicgeometers. For instance, the secant varieties of Veronese varieties are the loci obtained by setting allcovariance matrices to zero. We compute the ideals of the 5-dimensional moment varieties representingmixtures of two univariate Gaussians, and we oer a comparison to the maximum likelihood approach.

Connected Graphs Arising from Products of Veronese Varieties

Given a Segre squarefree Veronese configuration, following Bernd Sturmfels, we improve the study of the graphs associated to the configuration. We determine two special families of toric ideals and a finite set of moves for each of them, which still guarantee simultaneously the connection of all graphs arising from each family of moves.