Quadratic Counts of Twisted Cubics
Marc Levine, Sabrina Pauli
TL;DR
This paper introduces a quadratic refinement of counting twisted cubic curves on hypersurfaces using an advanced residue theorem, providing more detailed enumerative geometric information.
Contribution
It develops a quadratic version of the Bott residue theorem to refine counts of twisted cubics on hypersurfaces and complete intersections.
Findings
Quadratic refinement of twisted cubic counts
Application of a quadratic Bott residue theorem
Enhanced enumerative geometric results
Abstract
Using a quadratic version of the Bott residue theorem, we give a quadratic refinement of the count of twisted cubic curves on hypersurfaces and complete intersections in a projective space.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Mathematics and Applications