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Splitting Type, Global Sections and Chern Classes for Torsion Free Sheaves on P N
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bertone, Cristina Roggero, Margherita |
| Copyright Year | 2008 |
| Abstract | In this paper we compare a torsion free sheaf F on P N and the free vector bundle ' n=1 OPN(bi) having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the dierence are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes ci(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on P N , whose splitting type has no gap (i.e., bi ‚ bi+1 ‚ bi i 1 for every i = 1,...,n i 1), the following formula for the discriminant: ¢(F) := 2nc2 i (n i 1)c 2 ‚ i 1 12 n |
| Starting Page | 1147 |
| Ending Page | 1165 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.4134/JKMS.2010.47.6.1147 |
| Volume Number | 47 |
| Alternate Webpage(s) | https://arxiv.org/pdf/0804.2985v4.pdf |
| Alternate Webpage(s) | http://ocean.kisti.re.kr/downfile/volume/kms/DBSHBB/2010/v47n6/DBSHBB_2010_v47n6_1147.pdf |
| Alternate Webpage(s) | https://doi.org/10.4134/JKMS.2010.47.6.1147 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
