Table of Contents

## What is base locus of linear system of divisors?

The base locus of a linear system of divisors on a variety refers to the subvariety of points ‘common’ to all divisors in the linear system. Geometrically, this corresponds to the common intersection of the varieties.

## Which is an example of a system of linear equations?

A Systemof Linear Equations is when we have two or more linear equationsworking together. Example: Here are two linear equations: 2x y 5 −x y 2 Together they are a system of linear equations. Can you discover the values of xand yyourself? (Just have a go, play with them a bit.) Let’s try to build and solve a real world example:

## Which is a property of a linear system of divisors?

The Cayley–Bacharach theorem is a property of a pencil of cubics, which states that the base locus satisfies an “8 implies 9” property: any cubic containing 8 of the points necessarily contains the 9th. In general linear systems became a basic tool of birational geometry as practised by the Italian school of algebraic geometry.

## Which is the general representation of a linear equation?

The general representation of the straight-line equation is y=mx+b, where m is the slope of the line and b is the y-intercept. Linear equations are those equations that are of the first order. These equations are defined for lines in the coordinate system.

## Which is true of a linear system of divisors?

A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.

## Is the linear system of divisors an algebraic generalization?

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.

## Is the Kodaira-Spencer map the same as a linear system of divisors?

It is not to be confused with Kodaira–Spencer map from cohomology theory. A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles.