The geometry of complete linear maps
type: Item
instance of: scholarly article
title: The geometry of complete linear maps
zbMATH Open document ID: 0681.14034
DOI: 10.1007/BF02386122
published in: Arkiv för Matematik
publication date: 1988-01-01T00:00:00Z
review text: A complete linear map is a point of a certain compactification of the open subset \(L(E,F)'\) of the space L(E,F) of linear maps of vector spaces consisting of maps of maximal rank. Special cases are complete quadrics, complete collineations and correlations. The intersection theory on the parameter spaces of complete linear maps is used for justifications of some results in the enumerative geometry of the last century. The author gives a scheme-theoretical foundation of this theory. He generalizes an approach of J. Semple and J. Tyrrell in which a parameter space is obtained as the closure of the map \({\mathbb{P}}(L(E,F)')\to \prod_{i}(L(\bigwedge^ iE,\bigwedge^ iF)) \), \(\alpha \to (\alpha,\bigwedge^ 2\alpha,...)\). Instead of linear maps of vector spaces, the author considers a map \(E\to F\otimes L\), where E and F are vector bundles, and L is a line bundle over a scheme S.
Mathematics Subject Classification ID: 14N10
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 4114800
zbMATH Keywords: complete linear map
zbMATH Keywords: enumerative geometry
author: Dan Laksov
reviewed by: Igor V. Dolgachev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4114800