The homotopy type of spaces of rational curves on a toric variety

2017/07/09 by Andrzej Kozłowski, Kozlowski, Andrzej, Kohhei Yamaguchi +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1707.02603

Abstract

Spaces of holomorphic maps from the Riemann sphere to various complex manifolds (holomorphic curves ) have played an important role in several area of mathematics. In a seminal paper G. Segal investigated the homotopy type of holomorphic curves on complex projective spaces and M. Guest on compact smooth toric varieties.. Recently Mostovoy and Villanueva, obtained a far reaching generalisation of these results, and in particular (for holomorphic curves) improved the stability dimension obtained by Guest. In this paper, we generalize their result to holomorphic curves, on certain non-compact smooth toric varieties.

Related

• The topology of the space of rational curves on a toric variety
• Stability Theorems for Spaces of Rational Curves
• Homological Stability among Moduli Spaces of Holomorphic Curves in Complex Projective Space
• Spaces of non-resultant systems of bounded multiplicity determined by a toric variety
• Spaces of morphisms from a projective space to a toric variety