Rationality of cohomological descendent series for Quot schemes on surfaces with $p_g=0$
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910120463564800 |
|---|---|
| author | Anderson, Reginald |
| author_facet | Anderson, Reginald |
| contents | For a smooth projective surface $S$, Johnson, Oprea, and Pandharipande defined cohomological descendent generating series for the Quot schemes of rank-$0$ quotients of $\mathcal{O}_S^{\oplus N}$. We prove that these series are rational in the remaining surface case $p_g(S)=0$, $β\neq 0$, and $N>1$. The proof uses a fixed-source one-parameter wall-crossing recursion of Pandharipande-Thomas type, a factorization through pure Quot by two explicit zero-dimensional correction operators, a support-flat reduction of the first correction to relative Quot theory on curves, rationality of the resulting smooth and singular local curve factors, and a local $K$-theoretic vanishing that collapses the second correction to the universal punctual smooth-surface factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09738 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rationality of cohomological descendent series for Quot schemes on surfaces with $p_g=0$ Anderson, Reginald Algebraic Geometry 14N35, 14C05, 14D20, 14J60 For a smooth projective surface $S$, Johnson, Oprea, and Pandharipande defined cohomological descendent generating series for the Quot schemes of rank-$0$ quotients of $\mathcal{O}_S^{\oplus N}$. We prove that these series are rational in the remaining surface case $p_g(S)=0$, $β\neq 0$, and $N>1$. The proof uses a fixed-source one-parameter wall-crossing recursion of Pandharipande-Thomas type, a factorization through pure Quot by two explicit zero-dimensional correction operators, a support-flat reduction of the first correction to relative Quot theory on curves, rationality of the resulting smooth and singular local curve factors, and a local $K$-theoretic vanishing that collapses the second correction to the universal punctual smooth-surface factor. |
| title | Rationality of cohomological descendent series for Quot schemes on surfaces with $p_g=0$ |
| topic | Algebraic Geometry 14N35, 14C05, 14D20, 14J60 |
| url | https://arxiv.org/abs/2604.09738 |