On birational geometry of the space of parametrized rational curves in Grassmannians

2014/08/31 by Atsushi Ito, Ito, Atsushi
Mathematics · Physics and Astronomy · #14C20 #14M99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14C20 #msc:14M99

paper · pdf · doi:10.48550/arxiv.1409.0219

22 pages, Remark 5.9 in v1 replaced by Lemma 5.11. Accordingly, Theorems 1.5, 1.6 changed

openalex publication_date 2014/08/31 · arxiv created 2014/09/11 · arxiv updated 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the birational geometry of the Quot schemes of trivial bundles on ℙ¹ by constructing small ℚ-factorial modifications of the Quot schemes as suitable moduli spaces. We determine all the models which appear in the minimal model program on the Quot schemes. As a corollary, we show that the Quot schemes are Mori dream spaces and log Fano.

Related

• A Compactification of the Space of Parametrized Rational Curves in Grassmannians
• Birational geometry of smooth families of varieties admitting good minimal models
• Birational geometry of algebraic varieties
• The effective cone of the space of parametrized rational curves in a Grassmannian
• Compactified moduli spaces of rational curves in projective homogeneous varieties