Math Colloquium: "Unirational Parameterizations of Cubic Surfaces"Math Colloquium: "Unirational Parameterizations of Cubic Surfaces"http://www.haverford.edu/calendar/details/259937KINSC Hilles 109 2014-02-24T16:00:002014-02-24T17:00:00
February 24, 4:00PM–5:00PM
KINSC Hilles 109
Amanda Knecht (Villanova). KINSC H109.
Bi-College Math Colloquium
"Unirational Parameterizations of Cubic Surfaces"
Amanda Knecht, Villanova University.
Talk at 4 in KINSC H109
Tea at 3:30 in the Math Lounge (KINSC H208)
Abstract: A cubic surface is the zero set of a degree three homogeneous polynomial in four variables. For example, the Fermat cubic surface is defined by the vanishing of the equation x^3+y^3+z^3= w^3. It has been know for more than 100 years that for any smooth cubic surface X there is a one-to-one map between projective three space and X when the surface is defined over an algebraically closed field like the complex numbers. This is not true over non-closed fields like the real numbers. In 2002 Kollár proved that over any field there is a finite-to-one map from projective three space to X as long as there is at least one solution to the defining polynomial equation over that field. In this talk we will address the degree of that finite-to-one map for surfaces defined over finite fields.
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