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pro vyhledávání: '"Takahashi, Nobuyoshi"'
Autor:
Takahashi, Nobuyoshi
Let $T$ be a Lie-Yamaguti algebra whose standard enveloping Lie algebra $L(T)$ is semisimple and $[T, T, T]=T$. Then we give a description of representations of $T$ in terms of representations of $L(T)$ with certain additional data. Similarly, if $(T
Externí odkaz:
http://arxiv.org/abs/2407.16932
Autor:
Takahashi, Nobuyoshi
We study quandle modules over quandle spaces $Q$, i.e. quandles endowed with geometric structures. In the case $Q$ is a regular $s$-manifold, we exhibit how modules over $Q$ are related with representations of Lie-Yamaguti algebras.
Externí odkaz:
http://arxiv.org/abs/2010.05564
A great number of theoretical results are known about log Gromov-Witten invariants, but few calculations are worked out. In this paper we restrict to surfaces and to genus 0 stable log maps of maximal tangency. We ask how various natural components o
Externí odkaz:
http://arxiv.org/abs/1908.10906
Let $(S,E)$ be a log Calabi-Yau surface pair with $E$ a smooth divisor. We define new conjecturally integer-valued counts of $\mathbb{A}^1$-curves in $(S,E)$. These log BPS numbers are derived from genus 0 log Gromov-Witten invariants of maximal tang
Externí odkaz:
http://arxiv.org/abs/1810.02377
We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincare polynomials of the moduli spaces f
Externí odkaz:
http://arxiv.org/abs/1804.00679
Autor:
Takahashi, Nobuyoshi
Let $(Z, D)$ be a pair of a smooth surface and a smooth anti-canonical divisor. Denote by $\mathfrak{M}_\beta$ the moduli stack of genus $0$ relative stable morphisms of class $\beta$ with full tangency to the boundary. Let $C_1$ and $C_2$ be rationa
Externí odkaz:
http://arxiv.org/abs/1711.08173
Autor:
Takahashi, Nobuyoshi
Let $X$ be a normal, separated and integral scheme of finite type over $\mathbb{Z}$ and $\mathcal{M}$ a set of closed points of $X$. To a Galois cover $\tilde{X}$ of $X$ unramified over $\mathcal{M}$, we associate a quandle whose underlying set consi
Externí odkaz:
http://arxiv.org/abs/1508.03937
Autor:
Takahashi, Nobuyoshi
We define a quandle variety as an irreducible algebraic variety $Q$ endowed with an algebraically defined quandle operation $\rhd$. It can also be seen as an analogue of a generalized affine symmetric space or a regular $s$-manifold in algebraic geom
Externí odkaz:
http://arxiv.org/abs/1306.2396
Autor:
Takahashi, Nobuyoshi
Publikováno v:
Commun.Math.Phys. 220 (2001) 293-299
We study Mirror Symmetry of log Calabi-Yau surfaces. On one hand, we consider the number of ``affine lines'' of each degree in the complement of a smooth cubic in the projective plane. On the other hand, we consider coefficients of a certain expansio
Externí odkaz:
http://arxiv.org/abs/math/0004179
Autor:
Takahashi, Nobuyoshi
We show that counting functions of covers of $\mathbb{C}^\times$ are equal to sums of integrals associated to certain `Feynman' graphs. This is an analogue of the mirror symmetry for elliptic curves by Dijkgraaf.
Comment: 8 pages, 3 figures, AMS
Comment: 8 pages, 3 figures, AMS
Externí odkaz:
http://arxiv.org/abs/math/0004178