Properties of tautological classes and their intersections
| dc.contributor.author | Blankers, Vance T., author | |
| dc.contributor.author | Cavalieri, Renzo, advisor | |
| dc.contributor.author | Achter, Jeff, committee member | |
| dc.contributor.author | Pries, Rachel, committee member | |
| dc.contributor.author | Shoemaker, Mark, committee member | |
| dc.contributor.author | Heineman, Kristin, committee member | |
| dc.date.accessioned | 2019-06-14T17:06:40Z | |
| dc.date.available | 2019-06-14T17:06:40Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | The tautological ring of the moduli space of curves is an object of interest to algebraic geometers in Gromov-Witten theory and enumerative geometry more broadly. The intersection theory of this ring has a highly combinatorial structure, and we develop and exploit this structure for several ends. First, in Chapter 2 we show that hyperelliptic loci are rigid and extremal in the cone of effective classes on the moduli space of curves in genus two, while establishing the skeleton for similar results in higher genus. In Chapter 3 we connect the intersection theory of three families of important tautological classes (Ψ-, ω-, and κ-classes) at both the cycle and numerical level. We also show Witten's conjecture holds for κ-classes and reformulate the Virasoro operators in terms of κ-classes, allowing us to effectively compute relations in the κ-class subring. Finally, in Chapter 4 we generalize the results of the previous chapter to weighted Ψ-classes on Hassett spaces. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Blankers_colostate_0053A_15422_rev.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/195376 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.subject | intersection theory | |
| dc.subject | tautological ring | |
| dc.subject | algebraic geometry | |
| dc.subject | Witten's conjecture | |
| dc.subject | moduli space of curves | |
| dc.title | Properties of tautological classes and their intersections | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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