Mathematical Sciences: Research in Algebraic Geometry
{'Code': '03040300', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle'}
This project involves a variety of topics. Those concerning                regular finitely presented graded noncommutative algebras include               the investigation of these topics: (1) the correspondence between               algebras of dimension 3 and automorphisms of elliptic curves, (2)               the dualizing module, (3) the discovery, with the aid of a                      computer, of some new algebras of dimension 4 having two                        generators, (4) the constructability of the condition that an                   algebra be finite and of rank n over its center, and (5) the                    classification of those algebras via almost split sequences and                 via tilting equivalences. In geometry, the projects include the                 investigation of these topics: (1) the multiple-point theory of                 maps via the Hilbert scheme, (2) the structure and autoduality of               the relative compactified jacobian, (3) the classical enumerative               geometry of smooth plane cubics, (4) the Halphen intersection                   ring of a symmetric variety, (5) the degeneration of the tangent                space and Whitney stratification, (6) the positivity of the                     coefficients of Kazdan-Lusztig polynomials via intersection                     homology and the geometry of Schubert varieties (7) the stratum                 of the miniversal deformation space of a 2-dimensional                          hypersurface singularity as the hull of Wall's EF-functor, (8)                  the study of surfaces as projections, as subvarieties of 3-folds                of small degree, and as the carriers of important double                        structures, and (9) the study of L-functions of certain elliptic                curves over function fields via crytalline cohomology.                               This project concerns research on a variety of topics in                   algebraic geometry. After a long period of dormancy, this area of               mathematics has flourished with problems that are centuries old                 being resolved. The results of this research will be of interest                to many different areas of mathematics.
[{'FirstName': 'Steven', 'LastName': 'Kleiman', 'EmailAddress': 'KLEIMAN@MATH.MIT.EDU', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'Michael', 'LastName': 'Artin', 'EmailAddress': 'artin@math.mit.edu', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'Massachusetts Institute of Technology', 'CityName': 'Cambridge', 'ZipCode': '021394301', 'PhoneNumber': '6172531000', 'StreetAddress': '77 MASSACHUSETTS AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8801743.xml'}