Combinatorial Commutative Algebra
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ISBN-13:
9780387223568
Veröffentl:
2004
Einband:
HC runder Rücken kaschiert
Erscheinungsdatum:
21.12.2004
Seiten:
436
Autor:
Bernd Sturmfels
Gewicht:
816 g
Format:
241x160x28 mm
Serie:
227, Graduate Texts in Mathematics
Sprache:
Englisch
Beschreibung:
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.
This book provides an introduction to combinatorial commutative algebra with particular emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determined rings. The eighteen chapters cover 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. Contains over 100 figures and 250 exercises.
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.
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