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|Abstract:||We study families of elliptic curves whose coefficients are degree 2 polynomials in a variable t. All such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers. We prove that such conic bundles are unirational. As a consequence one obtains that, for infinitely many values of t, the resulting elliptic curve has rank at least 1.|
|Electronic Publication Date:||Aug-2017|
|Citation:||Kollar, Janos, Mella, Massimiliano. (2017). QUADRATIC FAMILIES OF ELLIPTIC CURVES AND UNIRATIONALITY OF DEGREE 1 CONIC BUNDLES. AMERICAN JOURNAL OF MATHEMATICS, 139 (915 - 936|
|Pages:||915 - 936|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||AMERICAN JOURNAL OF MATHEMATICS|
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