A short way of counting maps to hypersurfaces in Grassmannians

2025/06/12 by Marian, Alina, Sinha, Shubham · 1 citation
#14D20 #14M10 #14M15 #14N10 #14N35 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.10593

Abstract

Using a Quot scheme compactification, we calculate the virtual count of maps of degree d from a smooth projective curve of genus g to a hypersurface in a Grassmannian, sending specified points of the curve to special Schubert subvarieties restricted to the hypersurface. We study the question of whether this virtual count is in fact enumerative under suitable conditions on the hypersurface, in the regime when the map degree d is large.

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Cited by

• Intersection Theory of Hyperquot Schemes on curves

Related

• Asymptotic geometric Tevelev degrees of hypersurfaces
• Rational curves on Grassmannians: systems theory, reality, and transversality
• The Secant Conjecture in the real Schubert calculus
• Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian
• Enumerativity of virtual Tevelev degrees