Higher rank Segre integrals over the Hilbert scheme of points
| Autor: | Dragos Oprea, Rahul Pandharipande, Alina Marian |
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| Rok vydání: | 2021 |
| Předmět: |
Surface (mathematics)
Pure mathematics General Mathematics Vector bundle tautological integrals Rank (differential topology) 01 natural sciences law.invention Mathematics - Algebraic Geometry symbols.namesake Hilbert scheme of points Segre and Verlinde numbers Mathematics::Algebraic Geometry law 0103 physical sciences FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) Mathematics Series (mathematics) Applied Mathematics 010102 general mathematics Invertible matrix Hilbert scheme Euler's formula symbols 010307 mathematical physics |
| Zdroj: | Journal of the European Mathematical Society, 24 (8) |
| ISSN: | 1435-9855 1435-9863 |
| DOI: | 10.4171/jems/1149 |
| Popis: | Let S be a nonsingular projective surface. Each vector bundle V on S of rank s induces a tautological vector bundle over the Hilbert scheme of n points of S. When s = 1, the top Segre classes of the tautological bundles are given by a recently proven formula conjectured in 1999 by M. Lehn. We calculate here the Segre classes of the tautological bundles for all ranks s over all K-trivial surfaces. Furthermore, in rank s = 2, the Segre integrals are determined for all surfaces, thus establishing a full analogue of Lehn's formula. We also give conjectural formulas for certain series of Verlinde Euler characteristics over the Hilbert schemes of points. Journal of the European Mathematical Society, 24 (8) ISSN:1435-9855 ISSN:1435-9863 |
| Databáze: | OpenAIRE |
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