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REVIEW:
What is the intellectual merit of the proposed activity?
The PIs have led the recent most related research efforts in the
proposed area of algebraic geometry and geometric modeling. This
proposal should provide new theoretical foundations about Mu-bases
as the PIs are likely to achieve the goals the have set.
What are the broader impacts of the proposed activity?
The impact of this proposal is the only question mark I have as
the applications suggested by the PIs are quite narrow. Grobner
bases have found a wide range of applications (e.g. decoding of
algebraic geometry codes) , but there is no indications that
Mu-bases could reveal as useful while more efficient. The narrowness
of the focus of the proposal is better illustrated by the references
which are mainly the PIs' work or that of collaborators.
Summary Statement
The PIs give a clear and consice review of moving surfaces and
curves, syzygy modules, Mu-bases and their relationships, some
constituting recent results derived by the PIs. The applications
presented are confined to geometric modeling and the PIs rely on
their recent results in the field.
The PIs propose to investigate very relevant problems in the context
considered: rational surfaces and even rational curves. In particular
finding Mu-bases of rational surfaces (instead of the more widely
used Grobner bases) and determining their degree seems interesting.
If the PIs have clear ideas and directions to take about the first
problem, they mostly present goals for the second one. Nevertheless
in general, the PIs show a good grasp of the problems considered
and based on the directions they suggest, are convincing enough
about being able to achieve the goals they set.
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