5,190 research outputs found
On the Hodge conjecture for products of certain surfaces
No full textIn this thesis we prove the Hodge conjecture for products of smooth projective surfaces S(_1) x S(_2), where S(_2) = A is an Abelian surface and S (_1) is such that P(_g)(S(_1)) = 1, q = 2. We hereby provide new examples in dimension 4 where the Hodge conjecture holds
Acute Ethanol Administration Rapidly Increases Phosphorylation of Conventional Protein Kinase C in Specific Mammalian Brain Regions in Vivo
No full textBackground
Protein kinase C (PKC) is a family of isoenzymes that regulate a variety of functions in the central nervous system including neurotransmitter release, ion channel activity, and cell differentiation. Growing evidence suggests that specific isoforms of PKC influence a variety of behavioral, biochemical, and physiological effects of ethanol in mammals. The purpose of this study was to determine whether acute ethanol exposure alters phosphorylation of conventional PKC isoforms at a threonine 674 (p-cPKC) site in the hydrophobic domain of the kinase, which is required for its catalytic activity.
Methods
Male rats were administered a dose range of ethanol (0, 0.5, 1, or 2 g/kg, intragastric) and brain tissue was removed 10 minutes later for evaluation of changes in p-cPKC expression using immunohistochemistry and Western blot methods.
Results
Immunohistochemical data show that the highest dose of ethanol (2 g/kg) rapidly increases p-cPKC immunoreactivity specifically in the nucleus accumbens (core and shell), lateral septum, and hippocampus (CA3 and dentate gyrus). Western blot analysis further showed that ethanol (2 g/kg) increased p-cPKC expression in the P2 membrane fraction of tissue from the nucleus accumbens and hippocampus. Although p-cPKC was expressed in numerous other brain regions, including the caudate nucleus, amygdala, and cortex, no changes were observed in response to acute ethanol. Total PKC? immunoreactivity was surveyed throughout the brain and showed no change following acute ethanol injection
Mixed Hodge modules and real groups
No full textLet G be a complex reductive group, θ:G→G an involution, and K=Gθ. In [29], W. Schmid and the second named author proposed a program to study unitary representations of the corresponding real form GR using K-equivariant twisted mixed Hodge modules on the flag variety of G and their polarizations. In this paper, we make the first significant steps towards implementing this program. Our first main result gives an explicit combinatorial formula for the Hodge numbers appearing in the composition series of a standard module in terms of the Lusztig-Vogan polynomials. Our second main result is a polarized version of the Jantzen conjecture, stating that the Jantzen forms on the composition factors are polarizations of the underlying Hodge modules. Our third main result states that, for regular Beilinson-Bernstein data, the minimal K-types of an irreducible Harish-Chandra module lie in the lowest piece of the Hodge filtration of the corresponding Hodge module. An immediate consequence of our results is a Hodge-theoretic proof of the signature multiplicity formula of [2], which was the inspiration for this work
Mixed Hodge modules and real groups
No full textLet be a complex reductive group, an involution,
and . In arXiv:1206.5547, W. Schmid and the second named author
proposed a program to study unitary representations of the corresponding real
form using -equivariant twisted mixed Hodge modules on the
flag variety of and their polarizations. In this paper, we make the first
significant steps towards implementing this program. Our first main result
gives an explicit combinatorial formula for the Hodge numbers appearing in the
composition series of a standard module in terms of the Lusztig-Vogan
polynomials. Our second main result is a polarized version of the Jantzen
conjecture, stating that the Jantzen forms on the composition factors are
polarizations of the underlying Hodge modules. Our third main result states
that, for regular Beilinson-Bernstein data, the minimal -type of an
irreducible Harish-Chandra module lies in the lowest piece of the Hodge
filtration of the corresponding Hodge module. An immediate consequence of our
results is a Hodge-theoretic proof of the signature multiplicity formula of
arXiv:1212.2192, which was the inspiration for this work.Comment: 58 pages, including one appendix. v2: Added some references, minor
updates to the introductio
Effective classes in the projectivized k-th Hodge bundle:
No full textThesis advisor: Dawei ChenWe study the classes of several loci in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves and over the moduli space of genus g curves with n marked points. In particular we consider the class of the closure in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves with n marked points of the codimension n locus where the n marked points are zeros of the k-differential. We compute this class when n=2 and provide a recursive formula for it when n>2. Moreover, when n=1 and k=1,2 we show its rigidity and extremality in the pseudoeffective cone. We also compute the classes of the closures in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves of the loci where the k-differential has a zero at a Brill-Noether special point.Thesis (PhD) — Boston College, 2021.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Mathematics
TOWARDS A L 2 COHOMOLOGY THEORY FOR HODGE MODULES ON INFINITE COVERING SPACES: L 2 CONSTRUCTIBLE COHOMOLOGY AND L 2 DE RHAM COHOMOLOGY FOR COHERENT D-MODULES
No full textThis article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of Dingoyan's L 2-Mixed Hodge structures in terms of Saito's Mixed Hodge Modules and give partial results in this direction. 2020 AMS Classification: 32J27
Mixed Hodge modules on stacks
No full textUsing the -categorical enhancement of mixed Hodge modules constructed by the author in a previous paper, we explain how mixed Hodge modules canonically extend to algebraic stacks, together with all the operations and weights. We also prove that Drew\u27s approach to motivic Hodge modules gives an -category that embeds fully faithfully in mixed Hodge modules, and we identify the image as mixed Hodge modules of geometric origin.28 pages, comments welcome
Categories of complex variations of Hodge structure over compact K"ahler manifolds
No full textWe give a complex polarized variation of Hodge structure over a compact
K"ahler manifold which controls all finite-dimensional complex polarized
variations of Hodge structure over and their tensor relations. As a
corollary, we obtain the cohomology algebra with values in a local system
admitting multiplicative Hodge structures.Comment: 12 pages. Comments welcom
Mixed Hodge modules on stacks
No full textUsing the -categorical enhancement of mixed Hodge modules constructed by the author in a previous paper, we explain how mixed Hodge modules canonically extend to algebraic stacks, together with all the operations and weights. We also prove that Drew's approach to motivic Hodge modules gives an -category that embeds fully faithfully in mixed Hodge modules, and we identify the image as mixed Hodge modules of geometric origin
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