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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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Ample subvarieties and q-ample divisors
TL;DR: In this paper, the authors introduce a notion of ampleness for subschemes of higher codimension using the theory of q-ample line bundles, and investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz hyperplane theorems and numerical positivity.
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Degree and algebraic properties of lattice and matrix ideals
TL;DR: In this paper, the degree of nonhomogeneous lattice ideals over arbitrary fields was studied in terms of the torsion of certain factor groups of lattice polytopes.
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The basic geometry of Witt vectors. II: Spaces
TL;DR: In this article, the algebraic geometry of Witt vectors and arithmetic jet spaces is studied and the main point is to generalize this theory in two ways: the first is to allow not only p-typical Witt vectors but those taken with respect to any set of primes in any ring of integers in any global field, for example.
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Deformed Hamiltonian Floer theory, capacity estimates, and Calabi quasimorphisms
TL;DR: In this paper, a family of deformations of the differential and of the pair-of-pants product on the Hamiltonian Floer complex of a symplectic manifold (M,\omega) was developed, which upon passing to homology yields ring isomorphisms with the big quantum homology of M. This latter criterion is found to hold whenever M has generically semisimple quantum homologies in the sense considered by Dubrovin and Manin (this includes all compact toric M), and also whenever M is a point blowup of an arbitrary closed symp
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Coxeter and crystallographic arrangements are inductively free
Mohamed Barakat,Michael Cuntz +1 more
TL;DR: Using the classification of finite Weyl groupoids, the authors showed that all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type E 8.
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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: