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Thursday, July 26, 2018
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2:00pm [2:00pm]Dr. Vivek Mukundan
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Speaker : Dr. Vivek Mukundan Title : Implicitization problem and the defining ideal of the Rees algebra. When : Thursday 26 July, 2.00-3.30 pm 2 Aug 2.00-3.30 pm Venue: Room 215 ============= Abstract: Consider a rational map from P^{n-1}—>P^n parametrized by homogeneous polynomials f_0,\dots,f_n of degree d. We study the equations defining the graph of the map whose coordinate ring is the Rees algebra of the ideal generated by f_0, .., f_n. We provide new methods to construct these equations using work of Buchsbaum and Eisenbud. Furthermore, for certain classes of ideals, we show that our construction is general. These classes of examples are interesting, in that, there are no known methods to compute the defining ideal of the Rees algebra of such ideals. These new methods also give rise to effective criteria to check that φ is birational onto its image.

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