Matching of rigid shapes is an important problem in numerous applications across the boundary of computer vision, pattern recognition and computer graphics communities. A particularly challenging setting of this problem is partial matching, where the two shapes are dissimilar in general, but have significant similar parts. In this paper, we show an approach allowing to find matching parts of ri...

Matching of rigid shapes is an important problem in numerous applications across the boundary of computer vision, pattern recognition and computer graphics communities. A particularly challenging setting of this problem is partial matching, where the two shapes are dissimilar in general, but have significant similar parts. In this paper, we show a rigorous approach allowing to find matching par...

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomol-ogy. We establish the key properties of regularity: its connection with the ...

Associated to a projective arrangement of hyperplanes A ⊆ Pn is the module D(A), which consists of derivations tangent to A. We study D(A) when A is a configuration of lines in P. In this setting, we relate the deletion/restriction construction used in the study of hyperplane arrangements to elementary modifications of bundles. This allows us to obtain bounds on the Castelnuovo-Mumford regulari...

Abstract In this paper we study ideals of points lying on rational normal curves defined in projective plane and 3-space. We give an explicit formula for the value Castelnuovo–Mumford regularity their ordinary powers. Moreover, compare m -th symbolic powers such order to show whenever defect is non-zero.

Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated to reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also given ...