We give an elementary, explicit smooth compactification of a parameter space for the family of twisted cubics. The construction also applies to the family of subschemes defined by determinantal nets of quadrics, e.g., cubic ruled surfaces in P 4 , Segre varieties in P 5 . It is suitable for applications of Bott's formula to a few enumerative problems.

Recent years have seen an increase in the use of lignocellulosic materials in the development of bioproducts. Because sisal fiber is a low cost raw material and is readily available, this work aimed to evaluate its hemicellulose fraction for the simultaneous production of xylitol and ethanol. The sisal fiber presented a higher hemicellulose content than other frequently-employed biomasses, such as sugarcane bagasse. A pretreatment with dilute acid and low temperatures was conducted in order to obtain the hemicellulose fraction. The highest xylose contents (0.132 g·g−1 of sisal fiber) were obtained at 120 °C with 2.5% (v/v) of sulfuric acid. The yeast Candida tropicalis CCT 1516 was used in the fermentation. In the sisal fiber hemicellulose hydrolysate, the maximum production of xylitol (0.32 g·g−1) and of ethanol (0.27 g·g−1) was achieved in 60 h. Thus, sisal fiber presents as a potential biomass for the production of ethanol and xylitol, creating value with the use of hemicellulosic liquor without detoxification and without the additional steps of alkaline pretreatment.

We enumerate the cones over cubic scrolls satisfying appropriate incidence conditions to lines.

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We know from a result due to Noether–Lefschetz that a very general surface of degree at least 4 in [Formula: see text] contains only curves which are complete intersections with other surfaces. The main goal of this paper is to construct an explicit and smooth compactification of a parameter space for surfaces in [Formula: see text] of degree [Formula: see text] for all sufficiently large [Formula: see text], containing one conic and one line. The construction also applies to surfaces in [Formula: see text] containing one plane curve and one line. As an application, we compute the degree of the locus of surfaces of degree [Formula: see text] containing one conic and one line.

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We show how to compute the number of reducible cubic scrolls of codimension 2 in P n incident to the appropriate number of linear spaces.

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