Algebraicity of normal analytic compactifications of C^2 with one irreducible curve at infinity
| Autor: | Mondal, Pinaki |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Algebra Number Theory 10 (2016) 1641-1682 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2016.10.1641 |
| Popis: | We present an effective criterion to determine if a normal analytic compactification of C^2 with one irreducible curve at infinity is algebraic or not. As a by product we establish a correspondence between normal algebraic compactifications of C^2 with one irreducible curve at infinity and algebraic curves contained in C^2 with one place at infinity. Using our criterion we construct pairs of homeomorphic normal analytic surfaces with minimally elliptic singularities such that one of the surfaces is algebraic and the other is not. Our main technical tool is the sequence of "key forms" - a 'global' variant of the sequence of "key polynomials" introduced by MacLane to study valuations in the 'local' setting - which also extends the notion of "approximate roots" of polynomials considered by Abhyankar and Moh. Comment: Proof of Theorem 4.4 has been corrected - may thanks to the anonymous referee who pointed out the error. To appear in Algebra & Number Theory. arXiv admin note: text overlap with arXiv:1301.0126 |
| Databáze: | arXiv |
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