The concept of residual intersection, introduced by Artin and Nagata [l] in 1972, is a fruitful generalization of linkage as the following two examples attest. Let I be a strongly Cohen-Macaulay ideal in a CohenMacaulay local ring R. If Z satisfies the condition (G,), then Huneke [6, Proposition 4.31 has proved that the extended Rees algebra R[It, t‘1 is defined by an ideal which is obtained fr...

The intersection between 3D objects plays a prominent role in spatial reasoning, and computer vision. Detection of intersection between objects can be based on the triangulated boundaries of the objects, leading to computing triangle-triangle intersection. Traditionally there are separate algorithms for cross and coplanar intersection. For qualitative reasoning, intersection detection is suffic...

A bstract The systematic program of heterotic line bundle model building has resulted in a wealth standard-like models (SLM) for particle physics. In this paper, we continue work the setting generalised Complete Intersection Calabi Yau (gCICY) manifolds. Using gCICYs constructed ref. [1], identify two geometries that, when combined with sums, are directly suitable GUT models. We then show that ...

The second Veronese ideal In contains a natural complete intersection Jn generated by the principal 2-minors of a symmetric (n× n)-matrix. We determine subintersections of the primary decomposition of Jn where one intersectand is omitted. If In is omitted, the result is the other end of a complete intersection link as in liaison theory. These subintersections also yield interesting insights int...