Variety of singular quadrics containing a projective curve

Abstract

We study the variety of quadrics of rank at most k in ℙ r , containing a general projective curve of genus g and degree d and show that it has the expected dimension in the range g-d+r≤1. By considering the loci where this expectation is not true, we construct new divisor classes in ℳ ¯ g,n . We use one of these classes to show that ℳ ¯ 15,9 is of general type.