AIS Algebraic Geometry (2016) - Speakers and Syllabus

Syllabus:

Name of the Speaker with affiliation	No. of Lectures (each of 1 ½ hrs)	Detailed Syllabus
Shreedhar Inamdar, ISI Bangalore	6	Noether normalization and Hilbert Nullstellensatz, affine space and closed subsets, irreducible sets, regular functions and regular maps, rational functions and rational maps. Products of quasi-projective varieties, image of a projective variety under a regular map is closed. Finite maps, geometric version of Noether normalization. Dimension theory.
Amit Tripathi, NISER Bhubaneswar	6	Projective space and closed subsets, quasiprojective varieties, regular functions and rational functions on quasiprojective varieties, regular maps between quasiprojective varieties. Local ring at a point, tangent space at a point, singular and non-singular points, the tangent cone. Power series expansions, local parameters at a point.
Umesh Dubey, IISc., Bangalore	6	Properties of nonsingular points Blow-ups and birational maps Normal varieties. Singularities of maps.
Manish Kumar, ISI Bangalore	6	Divisors. Divisors on curves The plane cubic.
Suresh Nayak, ISI Bangalore	6	Algebraic groups Differential forms, examples, applications Riemann Roch theorem
Jishnu Biwas, ISI Bangalore	6	Intersection number and applications Birational maps of surfaces Singularities of curves and surfaces

References:

1. Basic Algebraic Geometry (Vol. 1) – I. Shafarevich

Time-Table (with names of speakers and course associates/tutors):

SI – Shreedhar Inamdar, AT – Amit Tripathi, UD – Umesh Dube, MK – Manish Kumar, SN – Suresh Nayak, JB – Jishnu Biswas

Tutorial Assistants: