Abstract/Details

Combinatorial aspects of toric varieties


2007 2007

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Abstract (summary)

According to Batyrev the Mori cone of a smooth, complete and projective toric variety can be generated by primitive relations. A primitive relation comes from a primitive collection, which is a set of 1-dimensional cones of the fan Σ such that the whole collection {ρ1, ..., ρk} does not generate a cone in Σ, but every subset does. To prove Batyrev's smooth case you can relate wall collections and primitive collections. I generalize Batyrev's statement to the non-complete, non-smooth but simplicial case and to the non-simplicial case.

Lawrence toric varieties arise as GIT-quotients. Hausel and Sturmfels showed that the cohomology of Lawrence toric varieties is independent of the GIT parameter. I will give a different proof for this result. Moreover, I will show that a natural way of generalizing these varieties does not have independent cohomology anymore by presenting some counter-examples.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Algebraic geometry; Lawrence toric varieties; Mori cone; Primitive collection; Toric variety
Title
Combinatorial aspects of toric varieties
Author
von Renesse, Christine
Number of pages
118
Publication year
2007
Degree date
2007
School code
0118
Source
DAI-B 68/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549330318
Advisor
Cattani, Eduardo
Committee member
Braden, Tom; Cattani, Eduardo; Cox, David; Kastor, David
University/institution
University of Massachusetts Amherst
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3289222
ProQuest document ID
304844917
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304844917
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