Commutative Algebra seminar
Speaker: R. V. Gurjar (TIFR (retd))
Title: Automorphisms of algebraic varieties II
Time, day and date: 4:00:00 PM, Tuesday, January 21
Venue: Ramanujan Hall
Abstract:
Commutative Algebra seminar
In the first lecture we will discuss general results about diffeomorphisms (resp. biholomorphisms) of compact differentiable (resp. compact complex) manifolds, and general algebraic varieties.
In the second talk we will indicate a proof of an important result.
Theorem. Let X be a smooth projective variety of general type. Then the automorphism group of X is finite.
This applies to compact Riemann surfaces of genus > 1. Using this I will indicate the proof of Hurwitz's theorem:
Theorem. Let C be a compact Riemann surface of genus g > 1. Then Aut(C) has order at most 84(g-1). This bound is best possible.