633 research outputs found
Galois groups of Schubert problems via homotopy computation
Numerical homotopy continuation of solutions to polynomial equations is the
foundation for numerical algebraic geometry, whose development has been driven
by applications of mathematics. We use numerical homotopy continuation to
investigate the problem in pure mathematics of determining Galois groups in the
Schubert calculus. For example, we show by direct computation that the Galois
group of the Schubert problem of 3-planes in C^8 meeting 15 fixed 5-planes
non-trivially is the full symmetric group S_6006.Comment: 17 pages, 4 figures. 3 references adde
Hyperelliptic addition law
We construct an explicit form of the addition law for hyperelliptic Abelian
vector functions and . The functions and form a basis
in the field of hyperelliptic Abelian functions, i.e., any function from the
field can be expressed as a rational function of and .Comment: 18 pages, amslate
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