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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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Automorphisms of generalized Fermat curves
Rubén A. Hidalgo,Aristides Kontogeorgis,Maximiliano Leyton-Álvarez,Panagiotis Paramantzoglou +3 more
TL;DR: In this article, it was shown that the non-trivial elements of the generalized Fermat group coincide with the hyper-osculating points of the fiber product model under the assumption that the characteristic p is either zero or p > k n − 1.
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The universal Lie infinity-algebroid of a singular foliation
TL;DR: The universal Lie ∞-algebroid of the singular foliation as discussed by the authors is a Lie n-algebra for real analytic or holomorphic singular foliations that can be chosen, locally, to be a lie n-Algebra of the foliation.
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Smooth and irreducible multigraded Hilbert schemes
Diane Maclagan,Gregory G. Smith +1 more
TL;DR: In this article, it was shown that any multigraded Hilbert scheme is smooth and irreducible when the polynomial ring is Z [ x, y ], which establishes a conjecture of Haiman and Sturmfels.
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Euler classes: six-functors formalism, dualities, integrality and linear subspaces of complete intersections
Tom Bachmann,Kirsten Wickelgren +1 more
TL;DR: In this article, the authors derived integrality results for the Euler classes of algebraic vector bundles and gave formulas for local indices at isolated zeros, both in terms of the six-functors formalism of coherent sheaves and as an explicit recipe in the commutative algebra of Scheja and Storch.
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Moduli of products of stable varieties
TL;DR: In this paper, the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program, has been studied, and it has been shown that taking products gives a well-defined morphism from the product of moduli spaces of a stable variety to the modulus space of the stable variety.
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: