EAN: 9783319241647

SPRINGERBRIEFS IN MATHEMATICS ARITHMETICALLY ...

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.

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