Speaker: Mohan Swaminathan
Date: May 06, 2024
Affiliation: Stanford University

Abstract: For positive integers n, g and d, the moduli space M(n,g,d) of degree d holomorphic maps to CP^n from non-singular projective curves of genus g is smooth and irreducible for d > 2g-2. It is contained as an open subset within the compact moduli space K(n,g,d) of "stable maps", i.e., degree d holomorphic maps to CP^n from at-worst-nodal projective curves of arithmetic genus g. An undesirable feature of this very natural compactification is that M(n,g,d) is far from being dense in K(n,g,d). Concretely, this means that many stable maps are not "smoothable", i.e., they don't arise as limits of non-singular ones. In my talk, I will explain this phenomenon and a new sufficient condition for smoothability of stable maps, obtained in joint work with Fatemeh Rezaee.