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
GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves
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DOI: 10.1515/forum-2024-0043
Abstract: Abstract We study the quotient variety of the space of foliations on ℂ ℙ 2 {\mathbb{CP}^{2}} of degree 2 up to change of coordinates. We find the intersection Betti numbers of this variety. As… read more here.
Keywords: betti numbers; quartic plane; plane curves; foliations degree ... See more keywords
Betti numbers of edge ideals of some graphs with application to graphs assigned to groups
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DOI: 10.2298/fil2406185r
Abstract: The article presents the Betti numbers of multiple complete split-like graphs, clique stars and their generalization. As an applications, we also give the Betti numbers of the graphs defined on groups, like power graphs of… read more here.
Keywords: betti numbers; edge ideals; ideals graphs; graphs application ... See more keywords
On the gluing of germs of complex analytic spaces, Betti numbers, and their structure
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DOI: 10.4153/s0008439524000961
Abstract: Abstract In this paper, we introduce new classes of gluing of complex analytic space germs, called weakly large, large, and strongly large. We describe their Poincaré series and, as applications, we give numerical criteria to… read more here.
Keywords: betti numbers; spaces betti; analytic spaces; gluing germs ... See more keywords