Biliaisons élémentaires en codimension 2

Brane Induced Gravity: Codimension-2

We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG) in 6D. Among a large diversity of regulated codimension-2 branes, we find that for near-critical tensions branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent of the tension, b...

Elimination Theory in Codimension 2

Sparse elimination theory concerns the study of Chow forms and discriminants associated with toric varieties, that is, subvarieties of projective space which are parametrized by monomials (Sturmfels, 1993; Gel’fand et al., 1994). This theory has its origin in the work of Gel’fand et al. on multivariate hypergeometric functions (Gel’fand et al., 1989). The singularities of these functions occur ...

Lifting Problem in Codimension 2 and Initial Ideals

Syzygies of Codimension 2 Lattice Ideals

The study of semigroup algebras has a long tradition in commutative algebra. Presentation ideals of semigroup algebras are called toric ideals, in reference to their prominent role in geometry. In this paper we consider the more general class of lattice ideals. Fix a polynomial ring S = k[x1, . . . , xn] over a field k and identify monomials x in S with vectors a ∈ N. Let L be any sublattice of...

Einstein gravity on the codimension 2 brane?

We look at general brane worlds in six-dimensional Einstein-Gauss-Bonnet gravity. We find the general matching conditions for the brane world, which remarkably give precisely the four-dimensional Einstein equations for the brane, even when the extra dimensions are noncompact and have infinite volume. Relaxing regularity of the curvature in the vicinity of the brane, or having a thick brane, giv...