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Full-Text Articles in Algebraic Geometry
Computation Of Real Radical Ideals By Semidefinite Programming And Iterative Methods, Fei Wang
Computation Of Real Radical Ideals By Semidefinite Programming And Iterative Methods, Fei Wang
Electronic Thesis and Dissertation Repository
Systems of polynomial equations with approximate real coefficients arise frequently as models in applications in science and engineering. In the case of a system with finitely many real solutions (the $0$ dimensional case), an equivalent system generates the so-called real radical ideal of the system. In this case the equivalent real radical system has only real (i.e., no non-real) roots and no multiple roots. Such systems have obvious advantages in applications, including not having to deal with a potentially large number of non-physical complex roots, or with the ill-conditioning associated with roots with multiplicity. There is a corresponding, but more …
K-Theory Of Root Stacks And Its Application To Equivariant K-Theory, Ivan Kobyzev
K-Theory Of Root Stacks And Its Application To Equivariant K-Theory, Ivan Kobyzev
Electronic Thesis and Dissertation Repository
We give a definition of a root stack and describe its most basic properties. Then we recall the necessary background (Abhyankar’s lemma, Chevalley-Shephard-Todd theorem, Luna’s etale slice theorem) and prove that under some conditions a quotient stack is a root stack. Then we compute G-theory and K-theory of a root stack. These results are used to formulate the theorem on equivariant algebraic K-theory of schemes.