On Binomial Equations Defining Rational Normal Scrolls
نویسندگان
چکیده
منابع مشابه
On binomial equations defining rational normal scrolls
We show that a rational normal scroll can in general be set-theoretically defined by a proper subset of the 2-minors of the associated two-row matrix. This allows us to find a class of rational normal scrolls that are almost settheoretic complete intersections.
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Abstract. Consider a height two ideal, I, which is minimally generated by m homogeneous forms of degree d in the polynomial ring R = k[x, y]. Suppose that one column in the homogeneous presenting matrix φ of I has entries of degree n and all of the other entries of φ are linear. We identify an explicit generating set for the ideal A which defines the Rees algebra R = R[It]; so R = S/A for the p...
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Let A be the homogeneous coordinate ring of a rational normal scroll. The ring A is equal to the quotient of a polynomial ring S by the ideal generated by the two by two minors of a scroll matrix ψ with two rows and l catalecticant blocks. The class group of A is cyclic, and is infinite provided l is at least two. One generator of the class group is [J], where J is the ideal of A generated by t...
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ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2011
ISSN: 1005-3867,0219-1733
DOI: 10.1142/s100538671100006x