S[subscript n]-equivariant sheaves and Koszul cohomology
Purpose: We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin's Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dimensions. Methods: We show that an explicit resolution of a certain S[subscr...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer
2014
|
| Online Access: | http://hdl.handle.net/1721.1/91930 |
| _version_ | 1826193117255041024 |
|---|---|
| author | Yang, David H. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Yang, David H. |
| author_sort | Yang, David H. |
| collection | MIT |
| description | Purpose:
We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin's Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dimensions.
Methods:
We show that an explicit resolution of a certain S[subscript n]-equivariant sheaf is equivalent to a resolution appearing in the theory of Koszul cohomology.
Results:
Our methods easily show that the dimension K[subscript p,q](B,L) is a polynomial in d for L=dA+P with A ample and d large enough.
Conclusions:
This interpretation allows us to extract various pieces of information about asymptotic properties Kp,q for fixed p,q. |
| first_indexed | 2024-09-23T09:34:01Z |
| format | Article |
| id | mit-1721.1/91930 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:34:01Z |
| publishDate | 2014 |
| publisher | Springer |
| record_format | dspace |
| spelling | mit-1721.1/919302022-09-26T12:17:37Z S[subscript n]-equivariant sheaves and Koszul cohomology Yang, David H. Massachusetts Institute of Technology. Department of Mathematics Yang, David H. Purpose: We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin's Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dimensions. Methods: We show that an explicit resolution of a certain S[subscript n]-equivariant sheaf is equivalent to a resolution appearing in the theory of Koszul cohomology. Results: Our methods easily show that the dimension K[subscript p,q](B,L) is a polynomial in d for L=dA+P with A ample and d large enough. Conclusions: This interpretation allows us to extract various pieces of information about asymptotic properties Kp,q for fixed p,q. National Science Foundation (U.S.). Research Experience for Undergraduates (Program) 2014-11-26T17:20:18Z 2014-11-26T17:20:18Z 2014-11 2014-07 2014-11-20T16:05:02Z Article http://purl.org/eprint/type/JournalArticle 2197-9847 http://hdl.handle.net/1721.1/91930 Yang, David H. “S n -Equivariant Sheaves and Koszul Cohomology.” Mathematical Sciences 1, no. 1 (December 2014). en http://dx.doi.org/10.1186/s40687-014-0010-9 Research in the Mathematical Sciences http://creativecommons.org/licenses/by/2.0 David H Yang et al.; licensee BioMed Central Ltd. application/pdf Springer |
| spellingShingle | Yang, David H. S[subscript n]-equivariant sheaves and Koszul cohomology |
| title | S[subscript n]-equivariant sheaves and Koszul cohomology |
| title_full | S[subscript n]-equivariant sheaves and Koszul cohomology |
| title_fullStr | S[subscript n]-equivariant sheaves and Koszul cohomology |
| title_full_unstemmed | S[subscript n]-equivariant sheaves and Koszul cohomology |
| title_short | S[subscript n]-equivariant sheaves and Koszul cohomology |
| title_sort | s subscript n equivariant sheaves and koszul cohomology |
| url | http://hdl.handle.net/1721.1/91930 |
| work_keys_str_mv | AT yangdavidh ssubscriptnequivariantsheavesandkoszulcohomology |