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Algebraic geometry is a branch of ______ which classically studies zeros of multivariate polynomials.
Algebraic geometry is a branch of ______ which classically studies zeros of multivariate polynomials.
mathematics
Modern algebraic geometry is based on the use of abstract ______ techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.
Modern algebraic geometry is based on the use of abstract ______ techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.
algebraic
The fundamental objects of study in algebraic geometry are ______ varieties, which are geometric manifestations of solutions of systems of polynomial equations.
The fundamental objects of study in algebraic geometry are ______ varieties, which are geometric manifestations of solutions of systems of polynomial equations.
algebraic
Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane ______ curves.
Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane ______ curves.
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A point of the plane lies on an ______ curve if its coordinates satisfy a given polynomial equation.
A point of the plane lies on an ______ curve if its coordinates satisfy a given polynomial equation.
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