Algebraic geometry and projective differential geometry, Seoul National University concentrated lecture series, 1997

TL;DR

This paper provides an expanded overview of algebraic and projective differential geometry, updating classical results with new insights on varieties, invariants, and recognition problems in algebraic geometry.

Contribution

It offers an updated, comprehensive lecture series on algebraic and projective differential geometry, including new perspectives on homogeneous varieties, invariants, and recognition of special varieties.

Findings

Analysis of homogeneous varieties and their topology

Criteria for recognizing uniruled and homogeneous varieties

Insights into secant, tangential, and complete intersection varieties

Abstract

This is an expanded and updated version of a lecture series I gave at Seoul National University in September 1997. It is in some sense an update of the 1979 Griffiths and Harris paper with a similar title. I discuss: Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, When can a uniruled variety be smooth?, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, Systems of quadrics with tangential defects, Recognizing uniruled varieties, Recognizing intersections of quadrics, Recognizing homogeneous spaces, Complete intersections. This is a preliminary version, so please send me comments, corrections and questions.