Linear systems in $\mathbb{P}^2$ with base points of bounded multiplicity
نویسندگان
چکیده
منابع مشابه
Linear Systems in P2 with Base Points of Bounded Multiplicity
We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with multiple points of order 7 or less. This uses a well-known degeneration of the plane developed by Ciliberto and Miranda as well as a combinatorial game that arises from specializing points onto lines.
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We address the problem of computing the dimension of the space of plane curves of fixed degree and general multiple base points. A conjecture of Harbourne and Hirschowitz gives geometric meaning to when this dimension is larger than the expected dimension obtained from Riemann-Roch; specifically, the dimension is larger than expected if and only if the system has a multiple (−1)-curve in its ba...
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In this article we address the problem of computing the dimension of the space of plane curves of degree d with n general points of multiplicity m. A conjecture of Harbourne and Hirschowitz implies that when d ≥ 3m, the dimension is equal to the expected dimension given by the Riemann-Roch Theorem. Also, systems for which the dimension is larger than expected should have a fixed part containing...
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Conjectures for the Hilbert function hðn;mÞ and minimal free resolution of the mth symbolic power Iðn;mÞ of the ideal of n general points of P are verified for a broad range of values of m and n where both m and n can be large, including (in the case of the Hilbert function) for infinitely many m for each square n > 9 and (in the case of resolutions) for infinitely many m for each even square n...
متن کاملEmptiness of Homogeneous Linear Systems with Ten General Base Points
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2007
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-06-00447-4