157 research outputs found
The Fine Moduli Space of Representations of Clifford Algebras
Given a fixed binary form of degree over a field , the
associated \emph{Clifford algebra} is the -algebra , where
is the two-sided ideal generated by elements of the form with and arbitrary elements in .
All representations of have dimensions that are multiples of , and
occur in families. In this article we construct fine moduli spaces
for the irreducible -dimensional representations of for each . Our construction starts with the projective curve defined by the equation , and produces
as a quasiprojective variety in the moduli space
of stable vector bundles over with rank and degree ,
where denotes the genus of .Comment: Final version. To appear in Int. Math. Res. Not. IMR
Ulrich Bundles on Quartic Surfaces with Picard Number 1
In this note, we prove that there exist stable Ulrich bundles of every even
rank on a smooth quartic surface with Picard number 1.Comment: Final version. To appear in Comptes Rendus Mathematiqu
On Nori's Obstruction to Universal Bundles
Let be or SO(2n). We consider the moduli space of
semistable principal -bundles over a curve . Our main result is that if
is a Zariski open subset of then there is no universal bundle on
The Period-Index Problem of the Canonical Gerbe of Symplectic and Orthogonal Bundles
We consider regularly stable parabolic symplectic and orthogonal bundles over
an irreducible smooth projective curve over an algebraically closed field of
characteristic zero. The morphism from the moduli stack of such bundles to its
coarse moduli space is a -gerbe. We study the period and index of this
gerbe, and solve the corresponding period-index problem.Comment: 19 pages. Complete rewrite of the previous version, including
expanded results on the moduli of parabolic G-bundles. To appear in the
Journal of Algebra. Comments welcom
On representations of Clifford algebras of ternary cubic forms
In this article, we provide an overview of a one-to-one correspondence
between representations of the generalized Clifford algebra of a ternary
cubic form and certain vector bundles (called Ulrich bundles) on a cubic
surface . We study general properties of Ulrich bundles, and using a recent
classification of Casanellas and Hartshorne, deduce the existence of
irreducible representations of of every possible dimension.Comment: 9 pages, to appear in proceedings for the conference "New Trends in
Noncommutative Algebra: A Conference in Honor of Ken Goodearl's 65th
Birthday
Pfaffian quartic surfaces and representations of Clifford algebras
Given a nondegenerate ternary form of degree 4 over an
algebraically closed field of characteristic zero, we use the geometry of K3
surfaces and van den Bergh's correspondence between representations of the
generalized Clifford algebra associated to and Ulrich bundles on the
surface to construct a
positive-dimensional family of irreducible representations of
The main part of our construction, which is of independent interest, uses
recent work of Aprodu-Farkas on Green's Conjecture together with a result of
Basili on complete intersection curves in to produce simple
Ulrich bundles of rank 2 on a smooth quartic surface
with determinant This implies that every smooth quartic
surface in is the zerolocus of a linear Pfaffian, strengthening
a result of Beauville-Schreyer on general quartic surfaces.Comment: This paper contains a proof of the main result claimed in the
erroneous preprint arXiv:1103.0529. We also extend this result to all smooth
quartic surface
A Quantitative Analysis of Ownership-Induced Quality Gaps in The Long-Term Care Sector: Influences of Ownership Conversions, Self-Reporting, Regulatory Reforms, and the Covid-19 Pandemic
This dissertation presents a quantitative analysis of the association between ownership types and quality of services in the long-term care sector in the United States. The study employs dynamic difference-in-differences models to investigate the effects of for-profit ownership conversions on nursing home quality indicators by drawing on national-level panel data for the years between 2013 and 2021. Additionally, the adverse effects of information asymmetries are examined by comparing changes in government-inspected quality measures with changes in self-reported quality measures following a for-profit conversion of a nursing home. Furthermore, the impact of the recent regulatory changes implemented at the end of 2016 in the nursing home sector and the facility-level factors associated with the COVID-19 pandemic outcomes in nursing homes are examined with respect to the quality trends and differences in quality by ownership types. Lastly, this study explores the relationship between ownership and quality in assisted living facilities in the State of Georgia using state inspection data. Overall, this dissertation finds that for-profit ownership status is associated with worse quality outcomes among nursing homes and assisted living facilities, including adverse outcomes of the COVID-19 pandemic. Moreover, the analyses show that the recent regulatory reforms had little to no effect on improving the quality of nursing homes over time. The findings are discussed to help policymakers formulate new policies and effective regulations to improve the quality of long-term care
A QUANTITATIVE ANALYSIS OF OWNERSHIP-INDUCED QUALITY GAPS IN THE LONG-TERM CARE SECTOR: INFLUENCES OF OWNERSHIP CONVERSIONS, SELF-REPORTING, REGULATORY REFORMS, AND THE COVID-19 PANDEMIC
This dissertation presents a quantitative analysis of the association between ownership types and quality of services in the long-term care sector in the United States. The study employs dynamic difference-in-differences models to investigate the effects of for-profit ownership conversions on nursing home quality indicators by drawing on national-level panel data for the years between 2013 and 2021. Additionally, the adverse effects of information asymmetries are examined by comparing changes in government-inspected quality measures with changes in self-reported quality measures following a for-profit conversion of a nursing home. Furthermore, the impact of the recent regulatory changes implemented at the end of 2016 in the nursing home sector and the facility-level factors associated with the COVID-19 pandemic outcomes in nursing homes are examined with respect to the quality trends and differences in quality by ownership types. Lastly, this study explores the relationship between ownership and quality in assisted living facilities in the State of Georgia using state inspection data. Overall, this dissertation finds that for-profit ownership status is associated with worse quality outcomes among nursing homes and assisted living facilities, including adverse outcomes of the COVID-19 pandemic. Moreover, the analyses show that the recent regulatory reforms had little to no effect on improving the quality of nursing homes over time. The findings are discussed to help policymakers formulate new policies and effective regulations to improve the quality of long-term care.Ph.D
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