k—Very Ample Line Bundles on Del Pezzo Surfaces

✍ Scribed by Sandra di Rocco

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 452 KB
• Volume: 179
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19961790104

✦ Synopsis

A k-very ample line bundle L on a Del Peaao Surface is numerically characterized, improving the results of BIANCOFIOR.E -CERESA in [7].

ample line bundles on surfaces whose Picard group is fully known. k -very ample line bundles on P2, on the Hirzebruch surfaces Fn and on hyperelliptic surfaces are indeed completely characterized in [3, 4, 111. This paper gives a numerical characterization of k-very ample line bundles on Del Pezzo surfaces, which improves the result of BIANCOFIORE and CERESA in [7].

Let S, be a Del Pezzo surface of degree 9 -T , i. e., -Ks, is an ample line bundle of degree 9 -r. We prove the following Theorem. Let L = a l -C T biei be a lane bundle on S, ,,,k+l)Ks, 1) ~O T T = 1, a 2 bl + k and bl 2 k; 2) f o r T = 2, 3, 4, bl 2 bz ... 2 b, 3 k and a 2 bi + b j + k, where i # j = 1, .