@article{737558,
      recid = {737558},
      author = {Guardo, Elena, and Van Tuyl, Adam,},
      title = {Arithmetically Cohen-Macaulay sets of points in P¹ × P¹  [electronic resource] /},
      pages = {1 online resource.},
      abstract = {This brief presents a solution to the interpolation  problem for arithmetically Cohen-Macaulay (ACM) sets of  points in the multiprojective space P̂1 x P̂1. 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 P̂1 x P̂1, the bigraded Hilbert function, and ACM  sets of points. The authors then show how, using a  combinatorial description of ACM points in P̂1 x P̂1, 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 P̂1 x P̂1 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.},
      url = {http://library.usi.edu/record/737558},
}