Titlebook: How Many Zeroes?; Counting Solutions o Pinaki Mondal Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license

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Intersection multiplicity at the originic power series supported at ., . (see theorem . for the precise statement); in this chapter, we compute this minimum and give a Bernstein-Kushnirenko-type characterization of the systems which attain the minimum.

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Number of zeroes on the affine space I: (Weighted) Bézout theorems property that the weight of each variable is .. In sections . and . we establish more general versions of these results involving arbitrary weighted degrees as special cases of the extension of Bernstein’s theorem to

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2730-650X loping all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students. .978-3-030-75176-0978-3-030-75174-6Series ISSN 2730-650X Series E-ISSN 2730-6518

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Textbook 2021oric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students. .

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