K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces
We study the holomorphic Euler characteristics of tautological sheaves on Hilbert schemes of points on surfaces. In particular, we establish the rationality of K-theoretic descendant series. Our approach is to control equivariant holomorphic Euler characteristics over the Hilbert scheme of points on...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2022 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211826 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces. Noah Arbesfeld. SIGMA 18 (2022), 078, 16 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862721982578032640 |
|---|---|
| author | Arbesfeld, Noah |
| author_facet | Arbesfeld, Noah |
| citation_txt | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces. Noah Arbesfeld. SIGMA 18 (2022), 078, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the holomorphic Euler characteristics of tautological sheaves on Hilbert schemes of points on surfaces. In particular, we establish the rationality of K-theoretic descendant series. Our approach is to control equivariant holomorphic Euler characteristics over the Hilbert scheme of points on the affine plane. To do so, we slightly modify a Macdonald polynomial identity of Mellit.
|
| first_indexed | 2026-03-21T04:21:11Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211826 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T04:21:11Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Arbesfeld, Noah 2026-01-12T10:21:58Z 2022 K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces. Noah Arbesfeld. SIGMA 18 (2022), 078, 16 pages 1815-0659 2020 Mathematics Subject Classification: 14C05; 14C17; 05E05 arXiv:2201.07392 https://nasplib.isofts.kiev.ua/handle/123456789/211826 https://doi.org/10.3842/SIGMA.2022.078 We study the holomorphic Euler characteristics of tautological sheaves on Hilbert schemes of points on surfaces. In particular, we establish the rationality of K-theoretic descendant series. Our approach is to control equivariant holomorphic Euler characteristics over the Hilbert scheme of points on the affine plane. To do so, we slightly modify a Macdonald polynomial identity of Mellit. I thank Lothar Gottsche, Anton Mellit, and Richard Thomas for feedback and related conversations, as well as Drew Johnson, Woonam Lim, Dragos Oprea, and Rahul Pandharipande for discussions and correspondence regarding Hilbert and Quot schemes. In particular, I thank Dragos Oprea for his suggestion to study the series(1.3). I also thank the anonymous referees for their feedback. This work was supported by the EPSRC through grant EP/R013349/1 and the NSF through grant DMS-1902717. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces Article published earlier |
| spellingShingle | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces Arbesfeld, Noah |
| title | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces |
| title_full | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces |
| title_fullStr | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces |
| title_full_unstemmed | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces |
| title_short | K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces |
| title_sort | k-theoretic descendent series for hilbert schemes of points on surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211826 |
| work_keys_str_mv | AT arbesfeldnoah ktheoreticdescendentseriesforhilbertschemesofpointsonsurfaces |