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Free resolutions an...
Free resolutions and Lefschetz properties of some Artin Gorenstein rings of codimension four
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- Abdallah, Nancy (author)
- Högskolan i Borås,Akademin för textil, teknik och ekonomi
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Schenck, Hal (author)
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(creator_code:org_t)
- 2024
- 2024
- English.
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In: Journal of symbolic computation. - 0747-7171 .- 1095-855X. ; 121, s. 102257-102257
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- In (Stanley, 1978), Stanley constructs an example of an Artinian Gorenstein (AG) ring A with non-unimodal H-vector (1,13,12,13,1). Migliore-Zanello show in (Migliore and Zanello, 2017) that for regularity r=4, Stanley's example has the smallest possible codimension c for an AG ring with non-unimodal H-vector.The weak Lefschetz property (WLP) has been much studied for AG rings; it is easy to show that an AG ring with non-unimodal H-vector fails to have WLP. In codimension c=3 it is conjectured that all AG rings have WLP. For c=4, Gondim shows in (Gondim, 2017) that WLP always holds for r≤4 and gives a family where WLP fails for any r≥7, building on Ikeda's example (Ikeda, 1996) of failure for r=5. In this note we study the minimal free resolution of A and relation to Lefschetz properties (both weak and strong) and Jordan type for c=4 and r≤6.
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Artinian algebraGorenstein algebraLefschetz propertyJordan type
Publication and Content Type
- ref (subject category)
- art (subject category)
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