Betti numbers of curves and multiple-point loci. (English) Zbl 1508.14032
The author establishes the experimental evidence in [F.-O. Schreyer, in: Advances in algebra and geometry. Proceedings of the international conference on algebra and geometry, Hyderabad, India, December 7–12, 2001. New Delhi: Hindustan Book Agency. 263–278 (2003; Zbl 1029.14021)] proposing the value of the extremal Betti number of a curve possessing several pencils. In fact, the author provides some conditions, mainly on the pencils under which the proposed formula for the extremal Betti number holds true. The proof is along the study of Eagon-Northcott cycles of higher codimensions. In particular, he proves the existence of curves possessing two pencils of such type, and therefore with the expected exremal Betti number.
Reviewer: Hanieh Keneshlou (Leipzig)
MSC:
| 14H51 | Special divisors on curves (gonality, Brill-Noether theory) |
| 16E05 | Syzygies, resolutions, complexes in associative algebras |
Citations:
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