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  JP Journal of Algebra, Number Theory and Applications  
 ISSN: 0972-5555
 
 
 

     JP Journal of Algebra, Number Theory and Applications
    Volume 13, Issue 2, Pages 209 - 219 (April 2009)


REMARKS ON THE BORDIGA SCROLLS OF DEGREE TEN

Antonio Lanteri (Italy) and Vania Nannola (Italy)

Received January 12, 2009

References:



[1] W. Barth, Some properties of stable rank-2 vector bundles on Math. Ann. 226 (1977), 125-150.

[2] O. Bottema, A classification of rational quartic ruled surfaces, Geom. Dedicata 1 (1973), 349-355.

[3] F. Catanese and B. Wajnryb, The 3-cuspidal quartic and braid monodromy of degree 4 coverings, Projective Varieties with Unexpected Properties, Vol. 1056, C. Ciliberto et al., eds., W. de Gruyter, Berlin, 2005, pp. 113-129.

[4] S. Di Rocco and A. J. Sommese, Line bundles for which a projectivized jet bundle is a product, Proc. Amer. Math. Soc. 129 (2000), 1659-1663.

[5] W. L. Edge, The Theory of Ruled Surfaces, Cambridge University Press, Cambridge, 1931.

[6] F. Ghione and G. Sacchiero, Normal bundles of rational curves in Manuscripta Math. 33 (1980/81), 111-128.

[7] Ph. Griffiths and J. Harris, On Cayley’s explicit solution to Poncelet’s porism, Enseign. Math. (2) 24 (1978), 31-40.

[8] P. Ionescu, Embedded projective varieties of small invariants, III, Algebraic Geometry, L’Aquila, 1988, A. J. Sommese, A. Biancofiore and E. L. Livorni, eds., Lecture Notes in Math., Vol. 1417, Springer, Berlin, Heidelberg, 1990, pp. 138-154.

[9] V. A. Iskovskikh and Yu. G. Prokhorov, Fano Varieties, Algebraic Geometry V, Encycl. Math. Sci., Vol. 47, Springer, Berlin, 1999.

[10] A. Lanteri and H. Maeda, Projective manifolds of sectional genus three as zero loci of sections of ample vector bundles, Math. Proc. Cambridge Philos. Soc. 130 (2008), 109-118.

[11] H. Maeda, The threefold containing the Bordiga surface of degree ten as a hyperplane section, Math. Proc. Cambridge Philos. Soc. 145 (2008), 619-622.

[12] M. Manaresi, On the jumping conics of a semistable rank two vector bundle on Manuscripta Math. 69 (1990), 133-151.

Keywords and phrases: vector bundles on the projective plane, jumping line, jumping conic, scroll, Fano threefold.

 


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