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What is a good book on algebraic geometry, with focus on toric varieties, similar both in the philosophy and in the prestige of the authors to Modern Geometric Structures and Fields by Novikov and Taimanov?

My background is from theoretical and mathematical physics, and I need toric geometry for string theory and mirror symmetry applications.

Up to now, the best I could find was Toric Varieties by Cox, Little and Schenck.

Another paper I should mention is http://arxiv.org/abs/hep-th/0702063

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    $\begingroup$ I've been told the best reference on toric varieties is Danilov's exposition: maths.ed.ac.uk/~aar/papers/danilov.pdf $\endgroup$
    – user314
    Jul 25, 2013 at 10:18
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    $\begingroup$ Since your background is in physics, you may be interested in the Mirror Symmetry book by Hori, Katz, ... found here:claymath.org/library. The canonical book for a long time has been Fulton's Introduction to Toric Varieties. $\endgroup$
    – Andrew
    Jul 25, 2013 at 11:48

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Just now I'm studyng for an exam in Toric Geometry, and the professor suggested "Toric Varieties" by Cox, Little and Schenck, "Introduction to toric varietis" by Fulton and "Symplectic toric manifolds", which are notes by Cannas De Silva about a Symplectic point of view in Toric Geometry. I think that Fulton's book is beautiful, but the most complete is surely Cox, Little and Schenck's.

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Here's David Cox's website with a few notes pertaining to toric varieties (i.e. "What is a Toric Variety") . http://www3.amherst.edu/~dacox/

These notes are exercise free but do cover a lot of the same material as his book.

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