The Bertini irreducibility theorem for higher codimensional slices |
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| Institution: | Institute of Science and Technology, Am Campus 1, 3400 Klosterneuburg, Austria |
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| Abstract: | In 3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions. |
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| Keywords: | Bertini theorems Irreducible varieties Finite fields Lang–Weil bound Random sampling |
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