Exact Formulas for Invariants of Hilbert Schemes
| Autor: | Gillman, Nate, Gonzalez, Xavier, Schoenbauer, Matthew |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Res. Number Theory (2018) 4:39 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40993-018-0132-z |
| Popis: | A theorem of G\"ottsche establishes a connection between cohomological invariants of a complex projective surface $S$ and corresponding invariants of the Hilbert scheme of $n$ points on $S.$ This relationship is encoded in certain infinite product $q$-series which are essentially modular forms. Here we make use of the circle method to arrive at exact formulas for certain specializations of these $q$-series, yielding convergent series for the signature and Euler characteristic of these Hilbert schemes. We also analyze the asymptotic and distributional properties of the $q$-series' coefficients. Comment: 25 pages, 1 figure, Accepted for publication in Research in Number Theory |
| Databáze: | arXiv |
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