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Commutative Algebra I

Craig Huneke
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TLDR
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 typed

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Nash Problem for quotient surface singularities

TL;DR: An affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$ is given.
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Framed sheaves on projective stacks

TL;DR: In this paper, a moduli space for semistable framed sheaves with fixed Hilbert polynomial and an open subset of it was constructed for stable framed sheaves, which is a quasi-projective scheme.
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On Fujita's freeness conjecture in dimension 5

TL;DR: In this article, it was shown that K X + k A is basepoint-free for any integer k ≥ 6 for a smooth projective variety of dimension 5 and A an integral ample divisor on X.
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A theory of dormant opers on pointed stable curves ---a proof of Joshi's conjecture---

TL;DR: In this paper, a detailed and original account of the theory of opers defined on pointed stable curves in arbitrary characteristic and their moduli is presented. But this work is restricted to the case of O(n) opers.
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Intermediate Jacobians and rationality over arbitrary fields

TL;DR: In this paper, it was shown that a smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. The theory of intermediate Jacobians for geometrically rational three-folds over arbitrary, not necessarily perfect, fields was developed.
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: