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Projective invariants of projective structures and applications (1962)
| Content Provider | CiteSeerX |
|---|---|
| Author | Mumford, David |
| Description | The basic problem that I wish to discuss is this: if F is a variety, or scheme, parametrizing the set, or functor, of all structures of some type in projective Ti-spaee Pn, then the group PGL(n) of automorphisms of Pn acts on V. Then under what conditions does there exist a quotient or orbit space V/PGL(n), i.e. when can we construct enough "projective invariants " for these structures? For example, let V parametrize the set of hypersurfaces of degree m, with certain types of singularities; or let V parametrize the set of tri-canonical space curves of given genus, or even n-canonical surfaces with at most "negligible singularities " [1]; or let V parametrize the set of 0-cycles of degree m in Pn; or let V parametrize the set of all morphisms of a fixed scheme X into Pn. Moreover, I wish to illustrate how such questions are one essential step in several basic existence and construction problems of algebraic geometry. One approach to this problem is afforded by the invariant theory of the representations of reductive groups. Here you generalize the problem first: |
| File Format | |
| Language | English |
| Publisher Date | 1962-01-01 |
| Publisher Institution | 1963 Proc. Internat. Congr. Mathematicians |
| Access Restriction | Open |
| Subject Keyword | Group Pgl Tri-canonical Space Curve Several Basic Existence Fixed Scheme Projective Invariant Negligible Singularity Reductive Group Orbit Space Pgl Enough Projective Invariant N-canonical Surface Invariant Theory Pn Act Projective Structure Construction Problem Certain Type Essential Step Basic Problem Algebraic Geometry Projective Ti-spaee Pn |
| Content Type | Text |
| Resource Type | Article |
