# What Do You Know About Schubert Variety?

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
A
Community Contributor
Quizzes Created: 129 | Total Attempts: 39,791
Questions: 10 | Attempts: 121

Settings

Schubert variety is a concept primarily used in the algebraic geometry branch of mathematics.
It is a particular subvariety of a Grassmannian Gr(k, V), especially with singular points.
And varieties classified as Schubert variety form one of the most significant and widely studied classes of singular algebraic varieties.

• 1.

### In algebraic geometry, a Schubert variety belongs to a certain subvariety of what?

• A.

General algebraic functions

• B.

Grassmannian

• C.

Exponential functions

• D.

Gymmeenial

B. Grassmannian
Explanation
A Schubert variety belongs to a certain subvariety of the Grassmannian. The Grassmannian is a geometric object that represents all possible linear subspaces of a given vector space. Schubert varieties are subvarieties of the Grassmannian that are defined by certain conditions on the dimension of intersections of linear subspaces. Therefore, the correct answer is Grassmannian.

Rate this question:

• 2.

### Which classification of points is used to represent the theorem?

• A.

Singular points

• B.

Multiple points

• C.

Double points

• D.

Triple points

A. Singular points
Explanation
The classification of points used to represent the theorem is singular points. Singular points are points on a curve where the curve fails to be smooth or differentiable. They can be endpoints, cusps, or self-intersections of the curve. This classification is relevant to the theorem being discussed as it involves analyzing the behavior of the curve at these singular points.

Rate this question:

• 3.

### What does W represent?

• A.

Vector space

• B.

Scalar space

• C.

Scalar-Vector space

• D.

Work done

A. Vector space
Explanation
The letter "W" typically represents a vector space in mathematics. A vector space is a collection of vectors that can be added together and multiplied by scalars. It satisfies certain properties, such as closure under addition and scalar multiplication. Therefore, the correct answer is "Vector space."

Rate this question:

• 4.

### Which set of numbers does W cover?

• A.

Whole numbers

• B.

Real numbers

• C.

Complex numbers

• D.

Natural numbers

C. Complex numbers
Explanation
The set of complex numbers includes all real numbers and imaginary numbers. Since W covers all complex numbers, it also covers real numbers. However, it does not cover natural numbers or whole numbers, as these sets are subsets of the complex numbers.

Rate this question:

• 5.

### Which kind of field does W cover?

• A.

Global field

• B.

Local field

• C.

Arbitrary field

• D.

External field

C. Arbitrary field
Explanation
The correct answer is "Arbitrary field". This suggests that the field W can cover any type of field without any specific restrictions or limitations. It can encompass various fields such as global, local, or external fields depending on the context or requirements.

Rate this question:

• 6.

### Who invented the theorem?

• A.

Hermann Schubert

• B.

Aurick Schubert

• C.

Siegfried Schubert

• D.

A. Hermann Schubert
Explanation
Hermann Schubert is credited with inventing the theorem.

Rate this question:

• 7.

### What does B represent?

• A.

Basil subgroup

• B.

Borel subgroup

• C.

Bowen subgroup

• D.

Bastille subgroup

B. Borel subgroup
Explanation
The correct answer is Borel subgroup. In mathematics, a Borel subgroup is a specific type of subgroup that plays a significant role in algebraic groups and Lie groups. Borel subgroups are maximal solvable subgroups and have many important properties. Therefore, B represents the Borel subgroup in this context.

Rate this question:

• 8.

### What does P represent?

• A.

Parabolic subgroup

• B.

Parallel subgroup

• C.

• D.

Piscilla subgroup

A. Parabolic subgroup
Explanation
The correct answer is Parabolic subgroup. In mathematics, a parabolic subgroup is a subgroup of a given group that stabilizes a certain point in a projective space. This term is often used in the context of algebraic groups and Lie groups. It represents a subgroup that preserves a certain geometric structure, similar to how a parabola preserves its shape when translated or rotated.

Rate this question:

• 9.

### What does X represent?

• A.

Heterogeneous space

• B.

Homogeneous space

• C.

Effervescent space

• D.

Delinquent space

B. Homogeneous space
Explanation
X represents a homogeneous space. A homogeneous space is a mathematical concept that refers to a space where every point has the same properties or characteristics. In other words, the space is uniform and consistent throughout, without any variations or differences between its points. This is in contrast to a heterogeneous space, which would have varying properties or characteristics at different points. Therefore, X represents a space where all points are the same, making it a homogeneous space.

Rate this question:

• 10.

### What is X equal to?

• A.

P/G

• B.

P*G

• C.

P+G

• D.

G/P

D. G/P
Explanation
X is equal to G divided by P.

Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

• Current Version
• Mar 19, 2023
Quiz Edited by
ProProfs Editorial Team
• Jun 17, 2018
Quiz Created by