Secant Cumulants and Toric Geometry
نویسندگان
چکیده
منابع مشابه
Secant Varieties of Toric Varieties
If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...
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We show how to use information about the equations defining secant varieties to smooth projective varieties in order to construct a natural collection of birational transformations. These were first constructed as flips in the case of curves by M. Thaddeus via Geometric Invariant Theory, and the first flip in the sequence was constructed by the author for varieties of arbitrary dimension in an ...
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We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry involves hypersurfaces in toric varieties (such as P blown up at more than 3 points) presents a challenge for the brane picture. We also find a simple physical exp...
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Acknowledgements First and foremost, I would like to thank Philip Candelas for his invaluable help throughout my four years in Oxford. I also owe special thanks to Bogdan Florea, Marcos Mariño and Harald Skarke for stimulating and enjoyable collaborations on the research topics discussed in this thesis. many others for interesting mathematical physics discussions. Many thanks to my parents, who...
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1.1. Flag Manifolds. One of the best understood examples of algebraic varieties is the flag manifold. One is first interested in flag varieties as they are well-defined examples for many basic concepts. Besides this, however, one can find that they deserve individual attention, for they naturally arise in many circumstances, e.g. in the theory of characteristic classes of vector bundles, mirror...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2014
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnu056