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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