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Betti numbers of curves and multiple-point loci |
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| Institution: | 1. Department of Mathematics and Computer Science, Eindhoven University of Technology, De Groene Loper 5, 5612 AZ, Eindhoven, Netherlands;2. Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090, Wien, Austria;1. Department of Mathematics, Swansea University, Swansea University Bay Campus, Fabian Way, Swansea SA1 8EN, UK;2. Faculty of Mathematics, University of Bia?ystok, K. Cio?kowskiego 1M, 15-245 Bia?ystok, Poland;3. Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK;4. Département de Mathématique, Université Libre de Bruxelles, Bd du Triomphe, B-1050 Brussels, Belgium |
| Abstract: | We construct Eagon–Northcott cycles on Hurwitz space and compare their classes to Kleiman's multiple point loci. Applying this construction towards the classification of Betti tables of canonical curves, we find that the value of the extremal Betti number records the number of minimal pencils. The result holds under transversality hypotheses equivalent to the virtual cycles having a geometric interpretation. We analyze the case of two minimal pencils, showing that the transversality hypotheses hold generically. |
| Keywords: | Primary"} {"#name":"keyword" "$":{"id":"kw0020"} "$$":[{"#name":"text" "_":"16E05 secondary"} {"#name":"keyword" "$":{"id":"kw0040"} "$$":[{"#name":"text" "_":"14H51 |
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