17,252 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
On the anomaly of nonlocal symmetry in the chiral QED
We show that the anomaly of nonlocal symmetry can be canceled by the
well-known Wess-Zumino acton which cancels the gauge anomaly in the
two-dimensional chiral electrodynamics.Comment: 4 pages, latex, no figure
Diagrams for Legendrian VMRT
We describe varieties of minimal rational tangents on the wonderful symmetric
varieties. An irreducible component of a variety of minimal rational tangents
is a rational homogeneous space, and hence, we have a corresponding Dynkin
diagram expression. On the other hand, we have diagrams from the (marked) Kac
diagram of a symmetric space by marking adjacent nodes to the marked node,
similar to the case of rational homogeneous spaces. We note that the above two
diagrams coincide when the restricted root system is not of type A. This paper
is a memo for "minimal rational curves on complete symmetric varieties".Comment: 14pag
Portfolio Optimization with Relative Tail Risk
This paper proposes analytic forms of portfolio CoVaR and CoCVaR on the
normal tempered stable market model. Since CoCVaR captures the relative risk of
the portfolio with respect to a benchmark return, we apply it to the relative
portfolio optimization. Moreover, we derive analytic forms for the marginal
contribution to CoVaR and the marginal contribution to CoCVaR. We discuss the
Monte-Carlo simulation method to calculate CoCVaR and the marginal
contributions of CoVaR and CoCVaR. As the empirical illustration, we show
relative portfolio optimization with thirty stocks under the distress condition
of the Dow Jones Industrial Average. Finally, we perform the risk budgeting
method to reduce the CoVaR and CoCVaR of the portfolio based on the marginal
contributions to CoVaR and CoCVaR
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