Vector Bundles on Algebraic Curves

The Moduli Space of Vector Bundles

Flag Varieties and their Geometry

Geometric Invariant Theory

It provided a new framework for studying vector bundles.

It led to the development of new techniques for constructing vector bundles.

It helped to unify different approaches to the study of vector bundles.

All of the above

The set of all vector bundles on a smooth projective variety.

The set of all stable vector bundles on a smooth projective variety.

The set of all semistable vector bundles on a smooth projective variety.

The set of all vector bundles on a smooth projective variety that are generated by their global sections.

It provides a way to classify vector bundles.

It helps to study the geometry of vector bundles.

It can be used to construct new vector bundles.

All of the above

A homogeneous space associated to a semisimple Lie group.

A variety that is the quotient of a semisimple Lie group by a Borel subgroup.

A variety that is the quotient of a semisimple Lie group by a maximal torus.

A variety that is the quotient of a semisimple Lie group by a parabolic subgroup.

They are important in representation theory.

They are used in the study of algebraic groups.

They are used in the study of invariant theory.

All of the above

A theory that studies the action of a reductive group on a variety.

A theory that studies the stability of vector bundles.

A theory that studies the moduli space of vector bundles.

A theory that studies the geometry of flag varieties.

It provides a way to construct new varieties.

It helps to study the geometry of varieties.

It can be used to classify varieties.

All of the above

He developed a new theory of vector bundles on algebraic curves.

He proved the Grauert-Riemenschneider vanishing theorem.

He introduced the notion of a perverse sheaf.

All of the above

He was awarded the Shanti Swarup Bhatnagar Prize in 1976.

He was elected a Fellow of the Indian Academy of Sciences in 1978.

He was elected a Fellow of the Royal Society in 1990.

All of the above

University of Madras

Tata Institute of Fundamental Research

Harvard University

All of the above

K. G. Ramanathan

M. S. Narasimhan

David Mumford

All of the above

Professor Emeritus at the University of Madras

Professor Emeritus at the Tata Institute of Fundamental Research

Professor Emeritus at Harvard University

All of the above

Reading

Traveling

Listening to music

All of the above

Indian food

Chinese food

Italian food

All of the above