Mori's program for the moduli space of conics in Grassmannian

TL;DR

This paper completes Mori's program for the moduli space of degree 2 stable maps to Grassmannians, describing all birational models via moduli spaces, incidence varieties, and desingularization techniques.

Contribution

It provides a comprehensive description of all birational models of the moduli space of conics in Grassmannians, advancing understanding of its geometric structure.

Findings

Classification of all birational models

Explicit descriptions using moduli spaces and incidence varieties

Application of Kirwan's desingularization techniques

Abstract

We complete Mori's program for Kontsevich's moduli space of degree 2 stable maps to Grassmannian of lines. We describe all birational models in terms of moduli spaces (of curves and sheaves), incidence varieties, and Kirwan's partial desingularization.