Sheaf stable pairs, Quot-schemes, and birational geometry
Caucher Birkar, Jia Jia, and Artan Sheshmani
TL;DR
This paper connects the moduli theory of sheaf stable pairs with birational geometry, focusing on smooth projective curves, providing detailed analysis and calculations in low degrees, and outlining future research directions.
Contribution
It introduces a novel framework linking sheaf stable pairs to birational geometry and offers detailed calculations for curves, expanding understanding in both areas.
Findings
Detailed analysis of sheaf stable pairs on curves
Calculations of moduli in low degrees
Identification of future research problems
Abstract
In this paper we build bridges between moduli theory of sheaf stable pairs on one hand and birational geometry on the other hand. We will in particular treat moduli of sheaf stable pairs on smooth projective curves in detail and present some calculations in low degrees. We will also outline problems in various directions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology