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Tautological Rings of Moduli Spaces of Curves
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The purpose of this thesis is to study tautological rings of moduli spaces of curves. The moduli spaces of curves play an important role in algebraic geometry. The study of algebraic cycles on these spaces was started by Mumford. He introduced the notion of tautological classes on moduli spaces of curves. Faber and Pandharipande have proposed several deep conjectures about the structure of the tautological algebras. According to the Gorenstein conjectures these algebras satisfy a form of Poincaré duality.

The thesis contains three papers. In paper I we compute the tautological ring of the moduli space of stable n-pointed curves of genus one of compact type. We prove that it is a Gorenstein algebra.

In paper II we consider the classical case of genus zero and its Chow ring. This ring was originally studied by Keel. He gives an inductive algorithm to compute the Chow ring of the space. Our new construction of the moduli space leads to a simpler presentation of the intersection ring and an explicit form of Keel’s inductive result.

In paper III we study the tautological ring of the moduli space of stable n-pointed curves of genus two with rational tails. The Gorenstein conjecture is proved in this case as well.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2011. , vii, 34 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 2011:03
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-34310ISBN: 978-91-7501-043-4OAI: oai:DiVA.org:kth-34310DiVA: diva2:420360
Public defence
2011-06-15, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
QC 20110608Available from: 2011-06-08 Created: 2011-06-01 Last updated: 2011-06-08Bibliographically approved
List of papers
1. THE TAUTOLOGICAL RING OF Mct1,n
Open this publication in new window or tab >>THE TAUTOLOGICAL RING OF Mct1,n
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-34426 (URN)
Available from: 2011-06-08 Created: 2011-06-08 Last updated: 2011-06-08Bibliographically approved
2. The Chow ring of the moduli space of curves of genus zero
Open this publication in new window or tab >>The Chow ring of the moduli space of curves of genus zero
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-34427 (URN)
Available from: 2011-06-08 Created: 2011-06-08 Last updated: 2011-06-08Bibliographically approved
3. The tautological ring of the moduli space Mrt 2,n
Open this publication in new window or tab >>The tautological ring of the moduli space Mrt 2,n
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-34428 (URN)
Available from: 2011-06-08 Created: 2011-06-08 Last updated: 2011-06-08Bibliographically approved

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Tavakol, Mehdi
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