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Combinatorial Commutative Algebra

Buch | Hardcover
420 Seiten
2004
Springer-Verlag New York Inc.
978-0-387-22356-8 (ISBN)

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Combinatorial Commutative Algebra - Ezra Miller, Bernd Sturmfels
CHF 149,75 inkl. MwSt
Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained 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 hands-on 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.

Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional 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.

Reihe/Serie Graduate Texts in Mathematics ; 227
Zusatzinfo XIV, 420 p.
Verlagsort New York, NY
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 0-387-22356-8 / 0387223568
ISBN-13 978-0-387-22356-8 / 9780387223568
Zustand Neuware
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