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Higher Initial Ideals of Homogeneous Ideals (Paperback) Loot Price: R1,117
Discovery Miles 11 170
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# Higher Initial Ideals of Homogeneous Ideals (Paperback)

### Series: Memoirs of the American Mathematical Society

Loot Price R1,117 Discovery Miles 11 170

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Given a homogeneous ideal $I$ and a monomial order, one may form the initial ideal $\textnormal{in}(I)$. The initial ideal gives information about $I$, for instance $I$ and $\textnormal{in}(I)$ have the same Hilbert function. However, if $\mathcal I$ is the sheafification of $I$ one cannot read the higher cohomological dimensions $h^i({\mathbf P}^n, \mathcal I(\nu)$ from $\textnormal{in}(I)$. This work remedies this by defining a series of higher initial ideals $\textnormal{in}_s(I)$ for $s\geq0$. Each cohomological dimension $h^i({\mathbf P}^n, \mathcal I(\nu))$ may be read from the $\textnormal{in}_s(I)$. The $\textnormal{in}_s(I)$ are however more refined invariants and contain considerably more information about the ideal $I$. This work considers in particular the case where $I$ is the homogeneous ideal of a curve in ${\mathbf P}^3$ and the monomial order is reverse lexicographic.Then the ordinary initial ideal $\textnormal{in}_0(I)$ and the higher initial ideal $\textnormal{in}_1(I)$ have very simple representations in the form of plane diagrams. It enables one to visualize cohomology of projective schemes in ${\mathbf P}^n$. It provides an algebraic approach to studying projective schemes. It gives structures which are generalizations of initial ideals.

### General

 Imprint: American Mathematical Society Country of origin: United States Series: Memoirs of the American Mathematical Society Release date: June 1998 Authors: Gunnar Floystad Dimensions: 252 x 174mm (L x W) Format: Paperback Pages: 80 ISBN-13: 978-0-8218-0853-5 Categories: Books > Science & Mathematics > Mathematics > Algebra > General LSN: 0-8218-0853-2 Barcode: 9780821808535

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