Counting tropical rational space curves with cross-ratio constraints

نویسندگان

چکیده

Abstract This is a follow-up paper of Goldner (Math Z 297(1–2):133–174, 2021), where rational curves in surfaces that satisfy general positioned point and cross-ratio conditions were enumerated. A suitable correspondence theorem provided Tyomkin (Adv Math 305:1356–1383, 2017) allowed us to use tropical geometry, and, particular, degeneration technique called floor diagrams . also holds higher dimension. In the current paper, we introduce so-called show they allow determine number space conditions. The multiplicities such can be calculated by enumerating certain plane.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Counting Curves on Rational Surfaces

In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points). We rephrase their arguments in the language of maps, and extend them to other rational surfaces, and other specified intersections with a divisor. As applications, (i) we count irreducible curves on Hirzebruc...

متن کامل

Counting Real Rational Curves on K3 Surfaces

We provide a real analog of the Yau-Zaslow formula counting rational curves on K3 surfaces. ”But man is a fickle and disreputable creature and perhaps, like a chess-player, is interested in the process of attaining his goal rather than the goal itself.” Fyodor Dostoyevsky, Notes from the Underground.

متن کامل

Counting Nodes on Rational Plane Curves

In this paper, we consider polynomial parametrized curves in the affine plane k over an algebraically closed field k. Such curves are given by κ : k → k : t 7→ (x(t), y(t)), and may or may not contain singular points. The problem of how many singular points there are is of specific importance to the theory of polynomial knots, as it gives a bound on the degrees necessary to achieve a parametriz...

متن کامل

Strata of rational space curves

The μ-invariant μ = (μ1, μ2, μ3) of a rational space curve gives important information about the curve. In this paper, we describe the structure of all parameterizations that have the same μ-type, what we call a μ-stratum, and as well the closure of strata. Many of our results are based on papers by the second author that appeared in the commutative algebra literature. We also present new resul...

متن کامل

COUNTING TROPICAL ELLIPTIC PLANE CURVES WITH FIXED j-INVARIANT

In complex algebraic geometry, the problem of enumerating plane elliptic curves of given degree with fixed complex structure has been solved by R.Pandharipande [8] using Gromov-Witten theory. In this article we treat the tropical analogue of this problem, the determination of the number Etrop(d) of tropical elliptic plane curves of degree d and fixed “tropical j-invariant” interpolating an appr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Manuscripta Mathematica

سال: 2021

ISSN: ['0025-2611', '1432-1785']

DOI: https://doi.org/10.1007/s00229-021-01317-3