*- new book*

ISBN: 9780821808535

Given a homogeneous ideal $I$ and a monomial order, one may form the initial ideal $ extnormal{in}(I)$. The initial ideal gives information about $I$, for instance $I$ and $ extnormal{in}(I)$ have the same Hilbert function. However, if $mathcal I$ is the sheafification of $I$ one cannot read the higher cohomological dimensions $h^i({mathbf P}^n, mathcal I(; u)$ from $ extnormal{in}(I)$. This. Given a homogeneous ideal $I$ and a monomial order, one may form the initial ideal $ extnormal{in}(I)$. The initial ideal gives information about $I$, for instance $I$ and $ extnormal{in}(I)$ have the same Hilbert function. However, if $mathcal I$ is the sheafification of $I$ one cannot read the higher cohomological dimensions $h^i({mathbf P}^n, mathcal I(; u)$ from $ extnormal{in}(I)$. This work remedies this by defining a series of higher initial ideals $ extnormal{in} s(I)$ for $sgeq0$. Each cohomological dimension $h^i({mathbf P}^n, mathcal I(; u))$ may be read from the $ extnormal{in} s(I)$. The $ extnormal{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 $ extnormal{in} 0(I)$ and the higher initial ideal $ extnormal{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. Books, Science and Geography~~Mathematics~~Algebra, Higher Initial Ideals Of Homogeneous Ideals~~Book~~9780821808535~~Gunnar Floystad, , , , , , , , , ,, [PU: American Mathematical Society]

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Higher Initial Ideals of Homogeneous Ideals (Memoirs of the American Mathematical Society)

*- Paperback*

1998, ISBN: 0821808532

[EAN: 9780821808535], Neubuch, [PU: American Mathematical Society], Mathematics|Algebra|General, Mathematics|Group Theory, Mathematics|Topology, Brand new. We distribute directly for the publisher. 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 o

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Higher Initial Ideals of Homogeneous Ideals (Memoirs of the American Mathematical Society)

*- Paperback*

1998, ISBN: 9780821808535

American Mathematical Society, 1998-07. Paperback. New. Brand new. We distribute directly for the publisher. 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., American Mathematical Society, 1998-07

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Higher Initial Ideals of Homogeneous Ideals

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ISBN: 9780821808535

Higher Initial Ideals of Homogeneous Ideals Paperback New Books, Amer Mathematical Society

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Higher Initial Ideals of Homogeneous Ideals

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1998, ISBN: 9780821808535

Buch, Softcover, [PU: American Mathematical Society], American Mathematical Society, 1998

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# Higher Initial Ideals Of Homogeneous Ideals* - new book*

ISBN: 9780821808535

Given a homogeneous ideal $I$ and a monomial order, one may form the initial ideal $ extnormal{in}(I)$. The initial ideal gives information about $I$, for instance $I$ and $ extnormal{in}… More...

## Gunnar Floystad:

Higher Initial Ideals of Homogeneous Ideals (Memoirs of the American Mathematical Society)*- Paperback*

1998, ISBN: 0821808532

[EAN: 9780821808535], Neubuch, [PU: American Mathematical Society], Mathematics|Algebra|General, Mathematics|Group Theory, Mathematics|Topology, Brand new. We distribute directly for the … More...

Higher Initial Ideals of Homogeneous Ideals (Memoirs of the American Mathematical Society)

*- Paperback*

1998

## ISBN: 9780821808535

American Mathematical Society, 1998-07. Paperback. New. Brand new. We distribute directly for the publisher. Given a homogeneous ideal $I$ and a monomial order, one may form the initia… More...

Higher Initial Ideals of Homogeneous Ideals

*- new book*

ISBN: 9780821808535

Higher Initial Ideals of Homogeneous Ideals Paperback New Books, Amer Mathematical Society

Higher Initial Ideals of Homogeneous Ideals

*- Paperback*

1998, ISBN: 9780821808535

Buch, Softcover, [PU: American Mathematical Society], American Mathematical Society, 1998

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** Details of the book - Higher Initial Ideals of Homogeneous Ideals**

EAN (ISBN-13): 9780821808535

ISBN (ISBN-10): 0821808532

Paperback

Publishing year: 1998

Publisher: American Mathematical Society

Book in our database since 2007-10-17T16:05:49-04:00 (New York)

Detail page last modified on 2022-05-25T20:48:31-04:00 (New York)

ISBN/EAN: 0821808532

ISBN - alternate spelling:

0-8218-0853-2, 978-0-8218-0853-5

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