Morgan Sherman

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Given an ideal I and a weight vector w which partially orders monomials we can consider the initial ideal inw(I) which has the same Hilbert function. A well known construction carries this out via a one-parameter subgroup of a GLn+1 which can then be viewed as a curve on the corresponding Hilbert scheme. Galligo [Gal79] proved that if I is in generic(More)
Gotzmann’s Persistence states that the growth of an arbitrary ideal can be controlled by comparing it to the growth of the lexicographic ideal. This is used, for instance, in finding equations which cut out the Hilbert scheme (of subschemes of Pn with fixed Hilbert polynomial) sitting inside an appropriate Grassmannian. We introduce the notion of an(More)
In [Don05b] Donaldson gives three operators on a space of Hermitian metrics on a complex projective manifold: T, Tν , TK . Iterations of these operators converge to balanced metrics, and these themselves approximate constant scalar curvature metrics. In this paper we investigate the convergence properties of these iterations by examining the case of the(More)
for some nonnegative integer k and complex numbers a0, . . . , ak, b1, . . . , bk ∈ C. Trigonometric polynomials and their series counterparts, the Fourier series, play an important role in many areas of pure and applied mathematics and are likely to be quite familiar to the reader. When reflecting on the terminology, however, it is reasonable to wonder why(More)
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