367 research outputs found
Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1
Smooth Schubert varieties in rational homogeneous manifolds of Picard number
1 are horospherical varieties. We characterize standard embeddings of smooth
Schubert varieties in rational homogeneous manifolds of Picard number 1 by
means of varieties of minimal rational tangents. In particular, we mainly
consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians
and in the 20-dimensional -homogeneous manifold associated to a short
simple root.Comment: 22 page
K\"ahler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
The wonderful compactification of a symmetric homogeneous space of type
AIII for each is Fano, and its blowup along the unique
closed orbit is Fano if and Calabi-Yau if . Using a
combinatorial criterion for K-stability of smooth Fano spherical varieties
obtained by Delcroix, we prove that admits a K\"ahler-Einstein metric for
each and admits a K\"ahler-Einstein metric if and only if .Comment: 20 pages, 6 figures. arXiv admin note: text overlap with
arXiv:2011.12551, arXiv:2203.1105
K-stability of Gorenstein Fano group compactifications with rank two
We give a classification of Gorenstein Fano bi-equivariant compactifications
of semisimple complex Lie groups with rank two, and determine which of them are
equivariant K-stable and admit (singular) K\"{a}hler-Einstein metrics. As a
consequence, we obtain several explicit examples of K-stable Fano varieties
admitting (singular) K\"{a}hler-Einstein metrics. We also compute the greatest
Ricci lower bounds, equivalently the delta invariants for K-unstable varieties.
This gives us three new examples on which each solution of the K\"{a}hler-Ricci
flow is of type II.Comment: 33 pages, 8 figure
K\"{a}hler-Einstein metrics on smooth Fano symmetric varieties with Picard number one
Symmetric varieties are normal equivarient open embeddings of symmetric
homogeneous spaces, and they are interesting examples of spherical varieties.
We prove that all smooth Fano symmetric varieties with Picard number one admit
K\"{a}hler-Einstein metrics by using a combinatorial criterion for K-stability
of Fano spherical varieties obtained by Delcroix. For this purpose, we present
their algebraic moment polytopes and compute the barycenter of each moment
polytope with respect to the Duistermaat-Heckman measure.Comment: 13 pages, 6 figure
Placenta Therapy: Its Biological Role of Anti-Inflammation and Regeneration
Human placental extract has been used to treat fatigue, postmenopausal symptoms, wound healing, and growth retardation in Korea. Combined with acupuncture therapy, placental extract extends its therapeutic limit to pain control. Recently, we have reported acupuncture point injection (API) with placental extract modulated inflammation-involving pain symptoms in chronic pain diseases. In order to rehabilitate patients suffering from chronic pain and restricted joint mobility, placental extract was injected into acupuncture points localized on the joints, surrounding muscles acting in concert with the joints, and paravertebral muscles affecting the innervation of the joints. Here, we describe the pathology of pain syndromes including neck pain, back pain, shoulder pain, knee arthritis, fibromyalgia, and complex regional pain syndrome and propose methodology of APIs with placental extract in treating these pain diseases
Gating of memory encoding of time-delayed cross-frequency MEG networks revealed by graph filtration based on persistent homology
To explain gating of memory encoding, magnetoencephalography (MEG) was analyzed over multi-regional network of negative correlations between alpha band power during cue (cue-alpha) and gamma band power during item presentation (item-gamma) in Remember (R) and No-remember (NR) condition. Persistent homology with graph filtration on alpha-gamma correlation disclosed topological invariants to explain memory gating. Instruction compliance (R-hits minus NR-hits) was significantly related to negative coupling between the left superior occipital (cue-alpha) and the left dorsolateral superior frontal gyri (item-gamma) on permutation test, where the coupling was stronger in R than NR. In good memory performers (R-hits minus false alarm), the coupling was stronger in R than NR between the right posterior cingulate (cue-alpha) and the left fusiform gyri (item-gamma). Gating of memory encoding was dictated by inter-regional negative alpha-gamma coupling. Our graph filtration over MEG network revealed these inter-regional time-delayed cross-frequency connectivity serve gating of memory encoding
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