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Higher codimension cycles on the Hilbert scheme of three points on the projective plane

Authors:	Tim Ryan Alexander Stathis

Institution:	1. Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States of America;2. Department of Mathematics, University of Georgia, Athens, GA 30602, United States of America;1. Department of Mathematics, Pedagogical University of Cracow, Podchora??ych 2, PL-30-084 Cracow, Poland;2. Jagiellonian University, Faculty of Mathematics and Computer Science, ?ojasiewicza 6, PL-30-348 Cracow, Poland;1. Insituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, CEP: 05508–090, Brazil;2. Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Reitor João David Ferreira Lima, Florianópolis, SC, CEP: 88040–900, Brazil;3. Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal;4. University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova cesta 2, SI-1000 Ljubljana, Slovenia;5. Institute of Mathematics, Physics and Mechanics, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia;1. School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom;2. Department of Mathematics, University of Manchester, Oxford Road M13 6PL, United Kingdom

Abstract:	In this paper, we study the higher codimensional cycle structure of the Hilbert scheme of three points in the projective plane. In particular, we compute all Chern/Segre classes of all tautological bundles on it and compute the nef (effective) cones of cycles in codimensions 2 and 3 (dimensions 2 and 3).

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