We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Theorem: any special scroll is the projection of a canonical scroll and they allow to understand the classification of special scrolls in P N . Canonical scrolls correspond to the projective model of canonical geometrically ruled surfaces over a smooth curve. We also prove that the generic canonical scroll is projectively normal except in the hyperelliptic case and for very particular cases in the nonhyperelliptic situation.

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The resting haemodynamics of five types of small (19 mm) aortic valve prosthesis (2 bileaflet, 3 pericardial) were evaluated with Doppler echocardiography in 43 patients. Two received St Jude Medical and six CarboMedics bileaflet valves and 35 were given bioprostheses--16 Ionescu-Shiley, four Mitroflow and 15 Labcor-Santiago. No significant differences in peak or mean transvalvular pressure drop or in effective valve area were found between the bileaflet and the pericardial valves or among the three types of bioprosthesis. All but one of the bileaflet prostheses showed a characteristic regurgitation pattern, with two lateral and one central jet, and 16 (46%) of the bioprostheses showed central regurgitation, but in no case were these jets haemodynamically significant. Thus the 19 mm bileaflet and the studied pericardial prostheses all have satisfactory resting haemodynamics, and all are suitable for implanting in small aortic roots.

The aim of this paper is to obtain a classification of the scrolls in IP n which are defined by a one-dimensional family of lines meeting a certain set of linear spaces in IP n , a first classification for genus 0 and 1 is given in paper [1]. These ruled surfaces are called incidence scrolls, and such an indicated set is a base of the incidence scroll. In particular, we compute its degree and genus. For this, we define the fundamental incidence scroll to be the scroll in IP n formed by the lines which meet (2n − 3) IP n−2 's in general position. Then all the others incidence scrolls will be portions of degenerate forms of this. In this way, we can obtain all the incidence scrolls in IP n , n ≥ 3, with base in general position.

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