Unirational threefolds with no universal codimension $$2$$ 2 cycle

Unirational threefolds with no universal codimension 2 cycle

We prove that the general quartic double solid with k ≤ 7 nodes does not admit a Chow theoretic decomposition of the diagonal, (or equivalently has a nontrivial universal CH0 group,) and the same holds if we replace in this statement “Chow theoretic” by “cohomological”. In particular, it is not stably rational. We also deduce that the general quartic double solid with seven nodes does not admit...

Unirational threefolds with no universal codimension cycle

Weprove that the general quartic double solidwith k ≤ 7 nodes does not admit a Chow theoretic decomposition of the diagonal, (or equivalently has a nontrivial universal CH0 group,) and the same holds if we replace in this statement “Chow theoretic” by “cohomological”. In particular, it is not stably rational. We also deduce that the general quartic double solid with seven nodes does not admit a...

Low Codimension Fano–enriques Threefolds

Introduction In the 1970s, Reid introduced the graded rings method for the explicit classification of surfaces, which he used to produce a list of 95 K3 quasi-smooth hypersurfaces in weighted projective spaces (which were proved to be the only ones). Later, Fletcher used this method to create more lists of different weighted complete intersections. From the K3 surfaces he developed two lists of...

Cover vol.2, no.2 October 2005

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...