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Betti numbers of gr...
Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen-Macaulay case
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- Boij, Mats (författare)
- KTH,Matematik (Avd.)
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- Söderberg, Jonas (författare)
- KTH,Matematik (Avd.)
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KTH Matematik (Avd) (creator_code:org_t)
- 2012-07-05
- 2012
- Engelska.
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Ingår i: Algebra & Number Theory. - : Mathematical Sciences Publishers. - 1937-0652 .- 1944-7833. ; 6:3, s. 437-454
- Relaterad länk:
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http://msp.org/ant/2...
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https://urn.kb.se/re...
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https://doi.org/10.2...
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Abstract
Ämnesord
Stäng
- We use results of Eisenbud and Schreyer to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination of Betti diagrams of modules with a pure resolution. This implies the multiplicity conjecture of Herzog, Huneke, and Srinivasan for modules that are not necessarily Cohen-Macaulay and also implies a generalized version of these inequalities. We also give a combinatorial proof of the convexity of the simplicial fan spanned by pure diagrams.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- graded modules
- Betti numbers
- multiplicity conjecture
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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