query: subclass_of fano variety
supports: Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. In algebraic geometry, a projective variety over an algebraically closed field "k" is a subset of some projective "n"-space P over "k" that is the zero-locus of some finite family of homogeneous polynomials of "n" + 1 variables with coefficients in "k", that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of P. In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its origins in the classical birational geometry of surfaces studied by the Italian school, and is currently an active research area within algebraic geometry. In mathematics, birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles. In algebraic geometry , a Fano variety , introduced in ( Fano 1934 , 1942 ) , is a complete variety X whose anticanonical bundle KX * is ample . In this definition , one could assume that X is smooth over a field , but the minimal model program has also led to the study of Fano varieties with various types of singularities , such as terminal or klt singularities . In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate is . An example in three variables is . Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ordinary integers formula_1, and "p"-adic integers.
candidates: algebra algebraic variety area change family field geometry greek knowledge learning map mathematics model number poles polynomial program range structure study subject theory variety
answer: algebraic variety