TY  - BOOK
AU  - Guardo,Elena
AU  - Van Tuyl,Adam
ED  - SpringerLink (Online service)
TI  - Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
T2  - SpringerBriefs in Mathematics,
SN  - 9783319241661
AV  - QA251.3 
U1  - 512.44 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - mathematics
KW  - Algebraic Geometry
KW  - Commutative algebra
KW  - Commutative rings
KW  - Projective Geometry
KW  - Mathematics
KW  - Commutative Rings and Algebras
N1  - Introduction -- The Biprojective Space P^1 x P^1 -- Points in P^1 x P^1 -- Classification of ACM Sets of Points in P^1 x P^1 -- Homological Invariants -- Fat Points in P^1 x P^1 -- Double Points and Their Resolution -- Applications -- References
N2  - This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1.  It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas.  The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points.  The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem.  In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra.  Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research.  Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature
UR  - http://dx.doi.org/10.1007/978-3-319-24166-1
ER  -