Let X be a zero-dimensional scheme in p1 × p1. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the A...Let X be a zero-dimensional scheme in p1 × p1. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the ACM case, can be obtained by their Hilbert functions and depend only on their distributions of points in a grid of lines. Moreover, a minimal set of generators of the ideal of these schemes is given by curves split into the union of lines.展开更多
Abstract. We find the minimal free resolution of a fat star-configuration X in Pn of type （r, s,t） defined by general forms of degrees d1,...,dr, and show that a fat linear star- configuration X in P2 never has gene...Abstract. We find the minimal free resolution of a fat star-configuration X in Pn of type （r, s,t） defined by general forms of degrees d1,...,dr, and show that a fat linear star- configuration X in P2 never has generic Hilbert function if （s,t） ≠ （1, 1） or （2, 2）. These two results generalize the interesting results of [2].展开更多
The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative trans...The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative transformation of Wiener process is a Wiener process, too.展开更多
文摘Let X be a zero-dimensional scheme in p1 × p1. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the ACM case, can be obtained by their Hilbert functions and depend only on their distributions of points in a grid of lines. Moreover, a minimal set of generators of the ideal of these schemes is given by curves split into the union of lines.
文摘Abstract. We find the minimal free resolution of a fat star-configuration X in Pn of type （r, s,t） defined by general forms of degrees d1,...,dr, and show that a fat linear star- configuration X in P2 never has generic Hilbert function if （s,t） ≠ （1, 1） or （2, 2）. These two results generalize the interesting results of [2].
文摘The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative transformation of Wiener process is a Wiener process, too.
