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 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.
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 کاملCounting Curves on Toric Surfaces
A few years ago, Tzeng settled a remarkable conjecture of Goettsche on counting nodal curves on smooth surfaces, proving that the formulas are given by certain universal polynomials. At the same time, Ardila and Block used the tropical approach of Brugalle, Mihalkin and Fomin to count nodal curves on a certain class of (not necessarily smooth) toric surfaces, and obtained similar polynomiality ...
متن کاملSome Remarks on the Severi Varieties of Surfaces in P3
Continuing the work of Chiantini and Ciliberto (1999) on the Severi varieties of curves on surfaces in P3, we complete the proof of the existence of regular components for such varieties. 2000 Mathematics Subject Classification. 14H10, 14B07.
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2018
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2015-0059