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130626  eng 
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a 9780387271033

100 
1 

a Miller, Ezra

245 
0 
0 
a Combinatorial Commutative Algebra
h Elektronische Ressource
c by Ezra Miller, Bernd Sturmfels

250 


a 1st ed. 2005

260 


a New York, NY
b Springer New York
c 2005, 2005

300 


a XIV, 420 p
b online resource

505 
0 

a Monomial Ideals  Squarefree monomial ideals  Borelfixed monomial ideals  Threedimensional staircases  Cellular resolutions  Alexander duality  Generic monomial ideals  Toric Algebra  Semigroup rings  Multigraded polynomial rings  Syzygies of lattice ideals  Toric varieties  Irreducible and injective resolutions  Ehrhart polynomials  Local cohomology  Determinants  Plücker coordinates  Matrix Schubert varieties  Antidiagonal initial ideals  Minors in matrix products  Hilbert schemes of points

653 


a Geometry, algebraic

653 


a Algebraic Geometry

653 


a Commutative Rings and Algebras

653 


a Algebra

653 


a Combinatorics

653 


a Combinatorics

700 
1 

a Sturmfels, Bernd
e [author]

710 
2 

a SpringerLink (Online service)

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a Graduate Texts in Mathematics

856 


u https://doi.org/10.1007/b138602?nosfx=y
x Verlag
3 Volltext

082 
0 

a 512.44

520 


a Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a selfcontained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to handson tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers. Ezra Miller received his doctorate in 2000 from UC Berkeley. After two years at MIT in Cambridge and one year at MSRI in Berkeley, he is currently Assistant Professor at the University of Minnesota, Twin Cities. Miller was awarded an Alfred P. Sloan Dissertation Fellowship in 1999 and an NSF Postdoctoral Fellowship in 2000. Besides his mathematical interests, which include combinatorics, algebraic geometry, homological algebra, and polyhedral geometry, Miller is fond of music theory and composition, molecular biology, and ultimate frisbee. Bernd Sturmfels received doctoral degrees in 1987 from the University of Washington, Seattle and TU Darmstadt, Germany. After two postdoc years at the IMA in Minneapolis and RISCLinz in Austria, he taught at Cornell University before joining UC Berkeley in 1995, where he is now Professor of Mathematics and Computer Science. A leading experimentalist among mathematicians, Sturmfels has authored seven books and over 130 research articles in the areas of combinatorics, algebraic geometry, symbolic computation, and their applications, and he has mentored 16 doctoral students
