Here are some exercises that I would like you to work on,
taken from the book <i> Toric Varieties</i> by Cox, Little, and Schenck.
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Section 1.1:  5, 14
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Section 1.2:  14
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Section 1.3:  7, 11
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Section 2.1:  6
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Section 2.2:  6, 7, 10
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Section 3.2:  7
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Section 3.3:  6, 8, 9, 13
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Section 4.1:  5
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Section 4.2:  10, 13