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Commutative Algebra I
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A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.Abstract:
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typedread more
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Arcs and wedges on rational surface singularities
TL;DR: In this article, it was shown that any wedge centered at P α lifts to the minimal desingularization of the Nash map of a rational surface singularity over an algebraically closed field k of characteristic 0.
Posted Content
The maximum likelihood degree of Fermat hypersurfaces
TL;DR: In this paper, the authors studied the critical points of the likelihood function over the Fermat hypersurface and provided closed formulas for the maximum likelihood degree of any Fermat curve in the projective plane and of Fermat surfaces of degree 2 in any projective space.
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Distinct distances in the complex plane
Adam Sheffer,Joshua Zahl +1 more
TL;DR: In this article, it was shown that if a set of points in a line with a slope is contained in a point set, then each pair of points has complex distance 0.
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Deforming spaces of m-jets of hypersurfaces singularities
TL;DR: In this paper, it was shown that an embedded deformation of a hypersurface which admits a Simultaneous Embedded Resolution (SIR) admits a deformation that is non-degenerate with respect to the Newton Boundary Γ ( f ).
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Link between Noetherianity and the Weierstrass Division Theorem on some quasianalytic local rings
TL;DR: In the setting of well-behaved quasianalytic differentiable systems, this paper proved that the Weierstrass Division theorem holds in such systems if, and only if, the system is Noetherian.
References
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Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures: