We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower affine Applications the theory include construction normal bundles for weighted submanifolds, as well pairs submanifolds with clean intersection.

We study the closure of locus radical ideals in multigraded Hilbert scheme associated with a standard graded polynomial ring and function homogeneous coordinate points general position projective space. In case plane, we give sufficient condition for an ideal to be ideals. For space arbitrary dimension present necessary condition. The paper is motivated by border apolarity lemma which connects ...

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic of higher-order tensors subject to and genericity constraint. Reformulating this computational problem as system polynomial equations allows us leverage recent linear algebra tools from algebraic geometry. characterize complexity our in terms an property system—the multigraded regularity. prov...

The toric Hilbert scheme of a lattice L ⊆ Z is the multigraded Hilbert scheme parameterizing all ideals in k[x1, . . . , xn] with Hilbert function value one for every g in the grading monoid G = N/L. In this paper we show that if L is twodimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert...