ar X iv : m at h / 05 05 09 6 v 2 [ m at h . A G ] 1 0 M ay 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ONTHE LINE

ar X iv : m at h / 05 05 09 6 v 4 [ m at h . A G ] 7 N ov 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE I

In this paper we study the structure of the graded ring of projective invariants of n ordered points on the projective line CP. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of relati...

ar X iv : m at h / 05 05 09 6 v 1 [ m at h . A G ] 5 M ay 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE

In this paper we study the structure of the graded ring of projective invariants of n ordered points on the projective line CP. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of relati...

ar X iv : m at h / 05 05 09 6 v 5 [ m at h . A G ] 1 0 N ov 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE

In this paper we study the structure of the graded ring of pro-jective invariants of n ordered points on the projective line CP 1. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of rel...

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 05 05 51 6 v 1 [ m at h . G N ] 2 4 M ay 2 00 5 HEREDITY OF τ - PSEUDOCOMPACTNESS

S. Garćıa-Ferreira and H. Ohta gave a construction that was intended to produce a τ -pseudocompact space, which has a regular-closed zero set A and a regular-closed C-embedded set B such that neither A nor B is τ pseudocompact. We show that although their sets A, B are not regular-closed, there are at least two ways to make their construction work to give the desired example.