منابع مشابه
A 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...
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We analyze the quantum evolution of a weakly nonlinear resonator due to a classical near-resonant drive and damping. The resonator nonlinearity leads to squeezing and heating of the resonator state. Using a hybrid phase-space–Fock-space representation for the resonator state within the Gaussian approximation, we derive evolution equations for the four parameters characterizing the Gaussian stat...
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 present several examples where moments of creators and annihilators on an interacting Fock space may be realized as moments of creators and annihilators on a full Fock module. Motivated by this experience we answer the question, whether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense. We treat the problem in full algebraic generality. As a by-product...
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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 ...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2017
ISSN: 0024-6115
DOI: 10.1112/plms.12017