Enumeration of genus-three plane curves with a fixed complex structure
نویسندگان
چکیده
منابع مشابه
Enumeration of Genus-three Plane Curves with a Fixed Complex Structure
We give a practical formula for counting irreducible nodal genus-three plane curves with a fixed general complex structure on the normalization. As an intermediate step, we enumerate rational plane curves that have a (3, 4)-cusp.
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We express the genus-two fixed-complex-structure enumerative invariants of P and P in terms of the genus-zero enumerative invariants. The approach is to relate each genus-two fixedcomplex-structure enumerative invariant to the corresponding symplectic invariant.
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As another application of the degeneration methods of [V3], we count the number of irreducible degree d geometric genus g plane curves, with fixed multiple points on a conic E, not containing E, through an appropriate number of general points in the plane. As a special case, we count the number of irreducible genus g curves in any divisor class D on the blow-up of the plane at up to five points...
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We give a formula for the number of genus-two fixed-complex-structure degree-d plane curves passing through 3d−2 points in general position. This is achieved by completing Katz-Qin-Ruan’s approach. This paper’s formula agrees with the one obtained by the author in a completely different way.
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2005
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-04-00375-3