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Arithmetic of Blowup Algebras
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  • Cited by 39
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ståhl, Gustav Sædén 2018. An intrinsic definition of the Rees algebra of a module. Proceedings of the Edinburgh Mathematical Society, Vol. 61, Issue. 01, p. 13.

    Miranda-Neto, Cleto B. 2018. An effective avoidance principle for a class of ideals. Mathematische Zeitschrift, Vol. 288, Issue. 3-4, p. 935.

    Basili, Roberta 2017. On commuting varieties of upper triangular matrices. Communications in Algebra, Vol. 45, Issue. 4, p. 1533.

    Banisaeed, E. Rahmati, F. Ahmadi-Amoli, Kh. and Eghbali, M. 2017. On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers. Communications in Algebra, Vol. 45, Issue. 12, p. 5137.

    Flores-Méndez, A. Gitler, I. and Reyes, E. 2017. Implosive graphs: Square-free monomials on symbolic Rees algebras. Journal of Algebra and Its Applications, Vol. 16, Issue. 08, p. 1750145.

    MIRANDA–NETO, CLETO B. 2017. Analytic spread and non-vanishing of asymptotic depth. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 163, Issue. 02, p. 289.

    Hassanzadeh, Seyed Hamid and Naéliton, Jose 2016. Residual intersections and the annihilator of Koszul homologies. Algebra & Number Theory, Vol. 10, Issue. 4, p. 737.

    Ramos, Zaqueu and Simis, Aron 2015. On catalecticant perfect ideals of codimension 2. Journal of Algebra and Its Applications, Vol. 14, Issue. 03, p. 1550031.

    Costa, Barbara Simis, Aron and Ramos, Zaqueu 2014. A theorem about Cremona maps and symbolic Rees algebras. International Journal of Algebra and Computation, Vol. 24, Issue. 08, p. 1191.

    Silva, Adriana R. and Vainsencher, Israel 2014. Degree of the variety of pairs of nilpotent commuting matrices. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 45, Issue. 4, p. 837.

    Panyushev, Dmitri I. 2013. Commuting involutions of Lie algebras, commuting varieties, and simple Jordan algebras. Algebra & Number Theory, Vol. 7, Issue. 6, p. 1505.

    Imtiaz, Mariam and Schenzel, Peter 2013. On the Non-Cohen–Macaulayness of Certain Factorial Closures. Communications in Algebra, Vol. 41, Issue. 9, p. 3397.

    Hong, Jooyoun Simis, Aron and Vasconcelos, Wolmer V. 2012. The equations of almost complete intersections. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 43, Issue. 2, p. 171.

    Vasconcelos, Wolmer V. 2010. Length Complexity of Tensor Products. Communications in Algebra, Vol. 38, Issue. 5, p. 1743.

    Morey, Susan 2010. Depths of Powers of the Edge Ideal of a Tree. Communications in Algebra, Vol. 38, Issue. 11, p. 4042.

    Branco Correia, Ana L. and Zarzuela, Santiago 2009. On Equimultiple Modules. Communications in Algebra, Vol. 37, Issue. 6, p. 1949.

    Ha, Minh Lam and Morales, Marcel 2009. Fiber Cone of Codimension 2 Lattice Ideals. Communications in Algebra, Vol. 37, Issue. 1, p. 1.

    Kleppe, Jan and Miró-Roig, Rosa 2009. Ideals generated by submaximal minors. Algebra & Number Theory, Vol. 3, Issue. 4, p. 367.

    Pham, Thuy and Vasconcelos, Wolmer V. 2008. Complexity of the normalization of algebras. Mathematische Zeitschrift, Vol. 258, Issue. 4, p. 729.

    Giorgi, Erika 2006. On the Irreducible Components of the Form Ring and an Application to Intersection Cycles. Communications in Algebra, Vol. 34, Issue. 8, p. 2755.

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    Arithmetic of Blowup Algebras
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Book description

This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.


‘…an interesting collection of facts not easily found elsewhere.’

Source: Mathematika

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