Universal polynomials for Severi degrees of toric surfaces
نویسندگان
چکیده
منابع مشابه
Universal Polynomials for Severi Degrees of Toric Surfaces
The Severi variety parameterizes plane curves of degree d with δ nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of CP. Fomin and Mikhalkin (2009) proved the 1995 conjecture that for fixed δ, Severi degrees are eventually polynomial in d. In this paper, we study the Severi varieties corresponding to a large family ...
متن کاملA combinatorial analysis of Severi degrees
Based on results by Brugallé and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degreesN using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version of a special function associated to long-edge graphs which appeared in Fomin-Mikhalkin’s formula, and conjectured it to be linear. They have since proved their conjecture. At the same t...
متن کاملq-Floor Diagrams computing Refined Severi Degrees for Plane Curves
The Severi degree is the degree of the Severi variety parametrizing plane curves of degree d with δ nodes. Recently, Göttsche and Shende gave two refinements of Severi degrees, polynomials in a variable q, which are conjecturally equal, for large d. At q = 1, one of the refinements, the relative Severi degree, specializes to the (non-relative) Severi degree. We give a combinatorial description ...
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We illustrate an efficient new method for handling polynomial systems with degenerate solution sets. In particular, a corollary of our techniques is a new algorithm to find an isolated point in every excess component of the zero set (over an algebraically closed field) of any n by n system of polynomial equations. Since we use the sparse resultant, we thus obtain complexity bounds (for converti...
متن کاملOn Severi varieties on Hirzebruch surfaces
In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2013
ISSN: 0001-8708
DOI: 10.1016/j.aim.2013.01.002