Common Ramification Points of Pencils on Double Covering Curves

2004 ◽  
Vol 46 (1-2) ◽  
pp. 13-15
Author(s):  
E. Ballico ◽  
C. Keem
2021 ◽  
Vol 21 (2) ◽  
pp. 221-225
Author(s):  
Taro Hayashi

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.


1996 ◽  
Vol 36 (2) ◽  
pp. 229 ◽  
Author(s):  
GG Johns

Bunch trimming (removal of male bud and several distal hands from bunches soon after flowering), and double covering (use of 2 bunch covers simultaneously) of banana bunches that emerge during winter in northern New South Wales could have the potential to increase the size, and hence grade and price of harvested fruit. Consequently bunches were either trimmed to 6, 8 or 10 hands or left untrimmed (male bud retained), and either single or double bunch covers were applied on a commercial plantation on 3 occasions during winter, and the effects on fruit size and quality were recorded. Bunch emergence to bunch harvest interval was reduced by an average of 5 days by bunch trimming. Finger length increased with increasing severity of bunch trimming, with the average length for the top 6 hands increased by 2.3% (P<0.01) for the 10-hand treatment to 6.1% (P<0.001) for the 6-hand treatment. Finger weight increased with increasing severity of bunch trimming, with weights for the top 6 hands increased by up to 14% (P < 0.001) on the 6-hand treatment. Double covering increased finger weight of the top 6 hands by 4% (P < 0.01). Trimming to 10, 8 and 6 hands increased the yield per bunch of extra large grade fruit by 18, 23 and 39% respectively. Double covering did not affect the yield of extra large fruit significantly. After excluding hands suffering from the mixed ripe condition, the 6-hand treatment yielded 51% more marketable extra large fruit than untrimmed bunches. Potential profitability of the treatments depended on price scenario. When prices were low the 6-hand treatment appeared most profitable, but at higher prices the 10-hand treatment would be preferable. Double covering appeared not to be worthwhile for all price scenarios used.


2013 ◽  
Vol 57 (1) ◽  
pp. 145-173 ◽  
Author(s):  
Atanas Iliev ◽  
Ludmil Katzarkov ◽  
Victor Przyjalkowski

AbstractThis paper suggests a new approach to questions of rationality of 3-folds based on category theory. Following work by Ballard et al., we enhance constructions of Kuznetsov by introducing Noether–Lefschetz spectra: an interplay between Orlov spectra and Hochschild homology. The main goal of this paper is to suggest a series of interesting examples where the above techniques might apply. We start by constructing a sextic double solid X with 35 nodes and torsion in H3(X, ℤ). This is a novelty: after the classical example of Artin and Mumford, this is the second example of a Fano 3-fold with a torsion in the third integer homology group. In particular, X is non-rational. We consider other examples as well: V10 with 10 singular points, and the double covering of a quadric ramified in an octic with 20 nodal singular points. After analysing the geometry of their Landau–Ginzburg models, we suggest a general non-rationality picture based on homological mirror symmetry and category theory.


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