On projective varieties of almsot minimal degree
Any nondegenerate irreducible projective variety X in a projective space satisfies
the condition deg(X) > codim(X). Thus it is a natural problem to classify
all varieties X satisfying deg(X)=codim(X)+k for each k=1,2,3,... and to understand
their algebraic and geometric structure. X is called a variety of minimal degree if
deg(X)=codim(X)+1. Those varieties are classified more than one hundred years ago
by Bertini and Del Pezzo. In this talk, we will consider the above problem
for the next case, that is varieties X with deg(X)=codim(X)+2.