Semantic Scholar Open Access 2007 205 sitasi

Betti numbers of graded modules and cohomology of vector bundles

D. Eisenbud F. Schreyer

Lihat Sumber DOI

Abstrak

Mats Boij and Jonas Soederberg (math.AC/0611081) have conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring can be decomposed in a certain way as a positive linear combination of Betti tables of modules with pure resolutions. We prove, over any field, a strengthened form of their conjecture. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fan naturally associated to the Young lattice. We also characterize the rational cone of all cohomology tables of vector bundles on projective spaces in terms of the cohomology tables of "supernatural" bundles. This characterization is dual, in a certain sense, to our characterization of Betti tables.

Topik & Kata Kunci

Mathematics

Penulis (2)

D. Eisenbud

F. Schreyer

Format Sitasi

APA MLA BibTeX

Eisenbud, D., Schreyer, F. (2007). Betti numbers of graded modules and cohomology of vector bundles. https://doi.org/10.1090/S0894-0347-08-00620-6

Akses Cepat

Lihat di Sumber doi.org/10.1090/S0894-0347-08-00620-6

Informasi Jurnal

Tahun Terbit: 2007
Bahasa: en
Total Sitasi: 205×
Sumber Database: Semantic Scholar
DOI: 10.1090/S0894-0347-08-00620-6
Akses: Open Access ✓