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TitleOn the homology of two-dimensional elimination
Author(s) Jooyoun Hong, Aron Simis, Wolmer V. Vasconcelos
TypeArticle in Journal
AbstractWe study birational maps with empty base locus defined by almost complete intersection ideals. Birationality is shown to be expressed by the equality of two Chern numbers. We provide a relatively effective method for their calculation in terms of certain Hilbert coefficients. In dimension 2 the structure of the irreducible ideals–always complete intersections by a classical theorem of Serre–leads by a natural approach to the calculation of Sylvester determinants. We introduce a computer-assisted method (with a minimal intervention by the computer) which succeeds, in degree ≤5, in producing the full sets of equations of the ideals. In the process, it answers affirmatively some questions raised by Cox [Cox, D.A., 2006. Four conjectures: Two for the moving curve ideal and two for the Bezoutian. In: Proceedings of Commutative Algebra and its Interactions with Algebraic Geometry, CIRM, Luminy, France, May 2006 (available in CD media)].
KeywordsAlmost complete intersection, Birational map, Elimination, Rees algebra, Special fiber, Sylvester determinant
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717107001393
LanguageEnglish
JournalJournal of Symbolic Computation
Volume43
Number4
Pages275 - 292
Year2008
Edition0
Translation No
Refereed No
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