What Do You Know About Schubert Variety?

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| By AdeKoju

AdeKoju

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Quizzes Created: 129 | Total Attempts: 41,686

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1/10 Questions

In algebraic geometry, a Schubert variety belongs to a certain subvariety of what?
- General algebraic functions
- Grassmannian
- Exponential functions
- Gymmeenial

About This Quiz

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.

What Do You Know About Schubert Variety? - Quiz

2.

Which classification of points is used to represent the theorem?
- Singular points
- Multiple points
- Double points
- Triple points
Correct Answer

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.

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3.

What does W represent?
- Vector space
- Scalar space
- Scalar-Vector space
- Work done
Correct Answer

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."

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4.

Which set of numbers does W cover?
- Whole numbers
- Real numbers
- Complex numbers
- Natural numbers
Correct Answer

A. 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.

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5.

Which kind of field does W cover?
- Global field
- Local field
- Arbitrary field
- External field
Correct Answer

A. 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.

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6.

Who invented the theorem?
- Hermann Schubert
- Aurick Schubert
- Siegfried Schubert
- Adalgar Schubert
Correct Answer

A. Hermann Schubert

Explanation

Hermann Schubert is credited with inventing the theorem.

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7.

What does B represent?
- Basil subgroup
- Borel subgroup
- Bowen subgroup
- Bastille subgroup
Correct Answer

A. 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.

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8.

What does P represent?
- Parabolic subgroup
- Parallel subgroup
- Paradoxical subgroup
- Piscilla subgroup
Correct Answer

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.

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9.

What does X represent?
- Heterogeneous space
- Homogeneous space
- Effervescent space
- Delinquent space
Correct Answer

A. 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.

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10.

What is X equal to?
- P/G
- P*G
- P+G
- G/P
Correct Answer

A. G/P

Explanation

X is equal to G divided by P.

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