This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| Eisenbud–Harris | |
|---|---|
| Name | Eisenbud–Harris |
| Field | Algebraic Geometry |
| Notable works | Brill–Noether theory extensions, Limit linear series |
| Contributors | David Eisenbud; Joe Harris |
| Country | United States |
| Institutions | University of California, Berkeley; Harvard University; Duke University; Brown University |
Eisenbud–Harris
Eisenbud–Harris denotes a body of work and collaborative results in algebraic geometry associated with David Eisenbud and Joe Harris, centering on extensions of Brill–Noether theory and the theory of limit linear series. Their contributions tie into themes studied at institutions such as Princeton University, Harvard University, University of California, Berkeley, Massachusetts Institute of Technology, and interact with problems addressed by figures like Alexander Grothendieck, Jean-Pierre Serre, David Mumford, Arnaud Beauville, Phillip Griffiths, and William Fulton.
The phrase identifies a program initiated in the late 20th century by David Eisenbud and Joe Harris while at Harvard University and later at Brandeis University and University of California, Berkeley, respectively, building on classical results from Adolf Brill and Max Noether and modern frameworks developed by Bernard Teissier, Oscar Zariski, David Mumford, Grothendieck, and Jean-Louis Verdier. It formalizes extensions of Brill–Noether theory and the construction of limit linear series influenced by work at Institute for Advanced Study and conferences at Mathematical Sciences Research Institute and Banff International Research Station. Early precursors include studies by Maurice Auslander, John Tate, Igor Shafarevich, Sergey Novikov, and papers distributed at American Mathematical Society meetings.
Eisenbud–Harris results include precise theorems about existence, dimension, and smoothing of linear series on curves connecting to conjectures by Brill, Noether, and later formulations related to problems studied by Joe Harris, David Eisenbud, Robin Hartshorne, Ziv Ran, Florian Pop, Eduardo Esteves, and Mihnea Popa. Their limit linear series theorem interacts with classical statements from Castelnuovo and modern refinements by William Fulton, Robert Lazarsfeld, Claire Voisin, Mark Green, and Tony Scholl, addressing questions previously raised at International Congress of Mathematicians sessions attended by Michael Atiyah, Isadore Singer, Shing-Tung Yau, and Pierre Deligne.
Techniques attributed to Eisenbud–Harris have been applied to moduli problems studied at Deligne–Mumford moduli spaces, to questions on syzygies influenced by David Eisenbud and Mark Green, to degeneration methods used by Robin Hartshorne and E. Arbarello, and to intersection-theoretic calculations in the tradition of William Fulton and Robert MacPherson. Their framework informs work on Hurwitz spaces investigated by John Conway and Gunnar Carlsson, on compactifications inspired by Pierre Deligne and David Mumford, and on enumerative geometry problems tackled by Maxim Kontsevich and Edward Witten.
Canonical examples include limit linear series on special curves related to constructions by Castelnuovo, degenerations studied by Francesco Severi, and explicit families explored by Joe Harris, David Eisenbud, Edoardo Sernesi, Dennis Gaitsgory, and János Kollár. Explicit constructions draw on techniques from Noether curve classifications, on syzygy computations echoing David Eisenbud and Mark Green, and on liaison methods traced to Peskine and Lichtenbaum. They appear in comparative studies with examples from Griffiths–Harris treatments and case analyses by Claire Voisin and Robert Lazarsfeld.
Proof methods employed by Eisenbud–Harris combine degeneration and smoothing arguments aligned with approaches used by David Mumford and Grothendieck, use of cohomological tools championed by Jean-Pierre Serre and Alexander Grothendieck, and liaison and syzygy techniques developed by David Eisenbud and Mark Green. Their work leverages deformation theory practiced by Robin Hartshorne, intersection theory with foundations in William Fulton, and moduli-space constructions related to Pierre Deligne and David Mumford. Computational examples often invoke algorithms and software initiatives connected to David Eisenbud's work at the Mathematical Sciences Research Institute and collaborations with computational projects at Institute for Computational and Experimental Research in Mathematics.
The development involved collaborations and influences from a large network including David Eisenbud, Joe Harris, William Fulton, Robin Hartshorne, David Mumford, Alexander Grothendieck, Jean-Pierre Serre, Mark Green, Robert Lazarsfeld, Claire Voisin, Pierre Deligne, Edoardo Sernesi, Eduardo Esteves, Mihnea Popa, Tony Scholl, Gunnar Carlsson, János Kollár, Maxim Kontsevich, Edward Witten, Phillip Griffiths, Arnaud Beauville, Dennis Gaitsgory, Igor Shafarevich, Oscar Zariski, Bernard Teissier, Peskine, Lichtenbaum, Adolf Brill, Max Noether, Castelnuovo, Severi, and many contributors from seminars at Harvard University, Princeton University, Institute for Advanced Study, Mathematical Sciences Research Institute, and Banff International Research Station.