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- W3217213793 abstract "We study punctual Quot-schemes of projective curves, surfaces and Calabi--Yau fourfolds and the symmetry of their (virtual) invariants. Let $Y$ be a variety in the above three classes, $E_Yto Y$ a torsion-free sheaf and $text{Quot}_Y(E_Y,n)$ the quot-scheme. Under some assumptions in the 4-fold case, $text{Quot}_Y(E_Y,n)$ is projective and carries a virtual fundamental class. Our goal is to give a(n almost) complete description of these classes and tautological integrals over them. We use novel methods developed in arXiv:2102.01056 relying on the wall-crossing framework of Joyce which have not yet been applied to this setting. We summarize here the main results: -- We show that the virtual cobordism class of $text{Quot}_S(E_S,n)$ depends only on rank. This implies in particular that for computing virtual Euler characteristic we may reduced to the case $E_S=mathbb{C}^e$. item The quotient of generating series of tautological invariants is expressed in terms of a universal power-series and $c_1(E_S)$. This leads to a generalization of rationality statements where we additional determine the poles for the $chi_y$-genus. -- We study a new 12-fold correspondence relating invariants of Calabi--Yau fourfolds, surfaces and curves. This includes a correspondence between virtual Segre and Verlinde series and improves on the 8-fold correspondence observed in arXiv:2008.10661 . -- We study the higher rank Nekrasov genus and its cohomological limit both of which can be expressed in terms of the Mac-Mahon series $M(q) = prod_{n>0}(1-q^n)^{-n}$. Along the way, we proved a new combinatorial identity related to Lagrange inversion which appeared in the companion paper arXiv:2111.09868." @default.
- W3217213793 created "2021-12-06" @default.
- W3217213793 creator A5046257922 @default.
- W3217213793 date "2021-11-22" @default.
- W3217213793 modified "2023-09-23" @default.
- W3217213793 title "Wall-crossing for punctual Quot-schemes" @default.
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- W3217213793 hasPublicationYear "2021" @default.
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