Latest Achievements
Dr. Peter Goetz's article titled "Algebras Associated to Inverse Systems of Projective Schemes" has been accepted for publication and will appear in the journal Algebras and Representation Theory. The work, joint with Dr. Andrew Conner at Saint Mary's College, introduces a functorial and geometric construction which takes a connected graded algebra A as input, and gives as output an algebra B(A), which generalizes the twisted homogeneous coordinate ring of a 3-dimensional Artin-Schelter regular algebra. The algebra B(A) is defined in terms of the inverse system of truncated point schemes and spaces of global sections of certain sheaves on products of projective spaces. A key result of the paper determines when a canonically defined algebra morphism A ---> B(A) is injective or surjective in terms of local cohomology modules.
Dr. Peter Goetz's article titled "Algebras Associated to Inverse Systems of Projective Schemes" has been accepted for publication and will appear in the journal Algebras and Representation Theory. The work, joint with Dr. Andrew Conner at Saint Mary's College, introduces a functorial and geometric construction which takes a connected graded algebra A as input, and gives as output an algebra B(A), which generalizes the twisted homogeneous coordinate ring of a 3-dimensional Artin-Schelter regular algebra. The algebra B(A) is defined in terms of the inverse system of truncated point schemes and spaces of global sections of certain sheaves on products of projective spaces. A key result of the paper determines when a canonically defined algebra morphism A ---> B(A) is injective or surjective in terms of local cohomology modules.