scholarly journals Distance Optimization and the Extremal Variety of the Grassmann Variety

2016 ◽  
Vol 169 (1) ◽  
pp. 1-16 ◽  
Author(s):  
John Leventides ◽  
George Petroulakis ◽  
Nicos Karcanias
Keyword(s):  
Grassmann Variety

Surfaces in the Grassmann Variety G(1, 3)

1979 ◽  
Vol 77 (1) ◽  
pp. 15 ◽  
Author(s):  
Aigli Papantonopoulou
Keyword(s):  
Grassmann Variety

scholarly journals Curves in Grassmann varieties

1977 ◽  
Vol 66 ◽  
pp. 121-137 ◽  
Author(s):  
Aigli Papantonopoulou
Keyword(s):  
Normal Bundle ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Main Motivation ◽  
Grassmann Variety ◽  
Knowing That ◽  
Necessary And Sufficient

The following question was the main motivation of this paper : which are the necessary and sufficient conditions for a non-singular subvariety of a Grassmann variety to have an ample normal bundle. Knowing that a non-singular subvariety of a Grassmann variety has an ample normal bundle we can apply on it several well-known theorems.

Plücker Coordinates for Regular Chain Groups

1973 ◽  
Vol 25 (1) ◽  
pp. 117-126
Author(s):  
T. Kambayashi
Keyword(s):  
Projective Space ◽  
Algebraic Variety ◽  
Grassmann Variety ◽  
Plücker Coordinates ◽  
Regular Chain ◽  
One To One ◽  
Set Of Points

The theory of Plücker coordinates and Grassmann varieties is well-developed and well-known among the algebraic geometers. It gives a one-to-one correspondence between the set of all subspaces of a given dimension in the ambient projective space and the set of points on a certain projective algebraic variety called a Grassmann variety. The unacquainted can find the theory discussed in detail in Hodge-Pedoe [1, Chapters VII and XIV].

scholarly journals The special linear version of the projective bundle theorem

2014 ◽  
Vol 151 (3) ◽  
pp. 461-501 ◽  
Author(s):  
Alexey Ananyevskiy
Keyword(s):  
Polynomial Algebra ◽  
Characteristic Classes ◽  
Zero Section ◽  
Grassmann Variety ◽  
Special Linear ◽  
Bundle Theorem ◽  
Linear Version ◽  
Hopf Map ◽  
Ring Cohomology ◽  
Witt Groups

AbstractA special linear Grassmann variety $\text{SGr}(k,n)$ is the complement to the zero section of the determinant of the tautological vector bundle over $\text{Gr}(k,n)$. For an $SL$-oriented representable ring cohomology theory $A^{\ast }(-)$ with invertible stable Hopf map ${\it\eta}$, including Witt groups and $\text{MSL}_{{\it\eta}}^{\ast ,\ast }$, we have $A^{\ast }(\text{SGr}(2,2n+1))\cong A^{\ast }(pt)[e]/(e^{2n})$, and $A^{\ast }(\text{SGr}(k,n))$ is a truncated polynomial algebra over $A^{\ast }(pt)$ whenever $k(n-k)$ is even. A splitting principle for such theories is established. Using the computations for the special linear Grassmann varieties, we obtain a description of $A^{\ast }(\text{BSL}_{n})$ in terms of homogeneous power series in certain characteristic classes of tautological bundles.

scholarly journals COTANGENT BUNDLE TO THE GRASSMANN VARIETY

2015 ◽  
Vol 21 (2) ◽  
pp. 519-530 ◽  
Author(s):  
V. LAKSHMIBAI
Keyword(s):  
Cotangent Bundle ◽  
Grassmann Variety

scholarly journals A new characterization of the Bruhat decomposition

1982 ◽  
Vol 86 ◽  
pp. 131-153 ◽  
Author(s):  
Yoshifumi Kato
Keyword(s):  
Homogeneous Space ◽  
Parabolic Subgroup ◽  
Lie Group ◽  
Dimensional Subspace ◽  
Factor Space ◽  
Bruhat Decomposition ◽  
Maximal Parabolic Subgroup ◽  
Grassmann Variety ◽  
Simply Connected

By an algebraic homogeneous space, we mean the factor space X = G/P, where G is a simply-connected, complex, semi-simple Lie group and P is a parabolic subgroup of G. Many typical manifolds such as the projective spaces and the Grassmann varieties belong to this class of manifolds. For instance, the Grassmann variety G(k, n) can be expressed as SL(n + 1, C)/P, where P is a maximal parabolic subgroup of SL(n + 1, C) leaving a suitable k + 1 dimensional subspace invariant. In this paper, we devote ourselves to study the Bruhat decomposition of an algebraic homogeneous space X = G/P.

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