Regularity, Rees algebra, and Betti numbers of certain cover ideals
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DOI: 10.1007/s00013-020-01486-9
Abstract: Let $$S={\textsf {k}}[X_1,\dots , X_n]$$ S = k [ X 1 , ⋯ , X n ] be a polynomial ring, where $${\textsf {k}}$$ k is a field. This article deals with the defining ideal… read more here.
Keywords: algebra betti; regularity rees; rees algebra; betti numbers ... See more keywords
On the $${\ell }^2$$ℓ2-Betti numbers of universal quantum groups
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DOI: 10.1007/s00208-017-1531-5
Abstract: We show that the first $${\ell }^2$$ℓ2-Betti number of the duals of the free unitary quantum groups is one, and that all $${\ell }^2$$ℓ2-Betti numbers vanish for the duals of the quantum automorphism groups of… read more here.
Keywords: ell betti; universal quantum; quantum groups; numbers universal ... See more keywords
Pollicott-Ruelle Resonant States and Betti Numbers
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DOI: 10.1007/s00220-020-03793-2
Abstract: Given a closed orientable hyperbolic manifold of dimension \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ne 3$$\end{document}≠3 we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms… read more here.
Keywords: resonant states; usepackage; states betti; pollicott ruelle ... See more keywords
Graded Betti Numbers of Balanced Simplicial Complexes
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DOI: 10.1007/s40306-021-00449-8
Abstract: We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings S/I, where S is a polynomial ring and $I\subseteq… read more here.
Keywords: numbers balanced; graded betti; number; betti numbers ... See more keywords
Betti numbers of MCM modules over the cone of an elliptic normal curve
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DOI: 10.1016/j.jalgebra.2019.01.032
Abstract: We apply Orlov's equivalence to derive formulas for the Betti numbers of maximal Cohen-Macaulay modules over the cone an elliptic curve $(E,x)$ embedded into $\mathbb{P}^{n-1}$, by the full linear system $|\mathcal{O}(nx)|$, for $n>3$. The answers… read more here.
Keywords: modules cone; cone elliptic; betti numbers; mcm modules ... See more keywords
Perfect modules with Betti numbers (2,6,5,1)
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DOI: 10.1016/j.jalgebra.2022.02.005
Abstract: In 2018 Celikbas, Laxmi, Kraśkiewicz, and Weyman exhibited an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the Tor algebra. All previously known perfect… read more here.
Keywords: betti numbers; modules betti; perfect modules;
Minimal free resolutions for homogeneous ideals with Betti numbers 1, n, n,1
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DOI: 10.1080/00927872.2018.1552281
Abstract: Abstract We investigate the standard generalized Gorenstein algebras of homological dimension three, giving a structure theorem for their resolutions. Moreover in many cases we are able to give a complete description of their graded Betti… read more here.
Keywords: homogeneous ideals; betti numbers; resolutions homogeneous; free resolutions ... See more keywords