Question: Information: - In algebraic geometry , a Segre surface , studied by Corrado Segre ( 1884 ) and Beniamino Segre ( 1951 ) , is an intersection of two quadrics in 4 - dimensional projective space . They are rational surfaces isomorphic to a projective plane blown up in 5 points with no 3 on a line , and are del Pezzo surfaces of degree 4 , and have 16 rational lines . The term '' Segre surface '' is also occasionally used for various other surfaces , such as a quadric in 3 - dimensional projective space , or the hypersurface x_1 x_2 x_3 + x_2 x_3 x_4 + x_3 x_4 x_5 + x_4 x_5 x_1 + x_5 x_1 x_2 = 0 . \ , - 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. - In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus "any" two distinct lines in a projective plane intersect in one and only one point. - In mathematics, a real number is a value that represents a quantity along a line. The adjective "real" in this context was introduced in the 17th century by Rene Descartes, who distinguished between real and imaginary roots of polynomials. - 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 . - In mathematics, a del Pezzo surface or Fano surface is a two-dimensional Fano variety, in other words a non-singular projective algebraic surface with ample anticanonical divisor class. They are in some sense the opposite of surfaces of general type, which have ample canonical class. - 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. - In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in R passing through the origin. - In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a "point at infinity". The statement and the proof of many theorems of geometry are simplified by the resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exactly one point (there is no "parallel" case). - Mathematics (from Greek "mathma", 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 mathematics, a projective space can be thought of as the set of lines through the origin of a vector space "V". The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R denotes ordered pairs of real numbers, and R denotes ordered triplets of real numbers. Given the information, choose the subject and object entities that have the relation of 'subclass of'.
Answer:
segre surface , algebraic surface