A Lattice-Geometric Proof of Wedderburn’s Theorem

1993 ◽  
Vol 23 (3-4) ◽  
pp. 384-386 ◽  
Author(s):  
Stefan E. Schmidt
Keyword(s):  
Geometric Proof

A Geometric Proof of lim d →0 +(-dln d) = 0

1992 ◽  
Vol 23 (3) ◽  
pp. 209
Author(s):  
John H. Mathews
Keyword(s):  
Geometric Proof

A Geometric Proof of Machin's Formula

1990 ◽  
Vol 63 (5) ◽  
pp. 336
Author(s):  
Roger B. Nelsen
Keyword(s):  
Geometric Proof

scholarly journals Non-defectivity of Grassmannian bundles over a curve

2016 ◽  
Vol 27 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Insong Choe ◽  
George H. Hitching
Keyword(s):  
Vector Bundles ◽  
Manuscripta Math ◽  
Maximal Degree ◽  
Geometric Proof ◽  
Secant Varieties ◽  
Grassmann Bundle ◽  
Positive Rank

Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on vector bundles over a curve, Manuscripta Math. 133 (2010) 465–477, I. Choe and G. H. Hitching, Lagrangian sub-bundles of symplectic vector bundles over a curve, Math. Proc. Cambridge Phil. Soc. 153 (2012) 193–214]. From the non-defectivity, we also deduce an interesting feature of a general orthogonal bundle of even rank over [Formula: see text], contrasting with the classical and symplectic cases: a general maximal isotropic sub-bundle of maximal degree intersects at least one other such sub-bundle in positive rank.

The Koch Curve: A Geometric Proof

2007 ◽  
Vol 114 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Šime Ungar
Keyword(s):  
Geometric Proof ◽  
Koch Curve
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