Faltings heights over function fields of complex projective curves are modular invariants of families of curves.The question on minimized Faltings heights was raised by Mazur.In this note,we consider this question for...Faltings heights over function fields of complex projective curves are modular invariants of families of curves.The question on minimized Faltings heights was raised by Mazur.In this note,we consider this question for a simple class of families of hyperelliptic curves.We obtain a complete result of this question in this case.展开更多
In this paper, by constructing the one-to-one correspondence between its IFS and the quaternary fractional expansion, the n-th iteration analytical expression and the limit representation of the family of the Koch-typ...In this paper, by constructing the one-to-one correspondence between its IFS and the quaternary fractional expansion, the n-th iteration analytical expression and the limit representation of the family of the Koch-type curves with arbitrary angles are obtained. The distinction between our method and that of H. Sagan is that we provide the generation process analytically and represent it as a graph of a series function which looks like the Weierstrass function. With these arithmetic expressions, we further analyze and prove some of the fractal properties of the Koch-type curves such as the self-similarity, the HSlder exponent and with the property of continuous everywhere but differentiable nowhere. Then, we will show that the Koch- type curves can be approximated by different constructed generators. Based on the analytic transformation of the Koch-type curves, we also constructed more continuous but nowhere-differentiable curves represented by arithmetic expressions. This result implies that the analytical expression of a fractal has theoretical and practical significance.展开更多
In this paper, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a character...In this paper, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a characterization of pseudo-periodic maps with nontrivial fractional Dehn twist coefficients. We also obtain some uniform lower bounds of non-zero fractional Dehn twist coefficients.展开更多
基金Supported by NSFC(Grant No.12271073)Fundamental Research Funds of the Central Universities(Grant No.DUT18RC(4)065)。
文摘Faltings heights over function fields of complex projective curves are modular invariants of families of curves.The question on minimized Faltings heights was raised by Mazur.In this note,we consider this question for a simple class of families of hyperelliptic curves.We obtain a complete result of this question in this case.
基金Supported partly by National Natural Science Foundation of China(No.60962009)
文摘In this paper, by constructing the one-to-one correspondence between its IFS and the quaternary fractional expansion, the n-th iteration analytical expression and the limit representation of the family of the Koch-type curves with arbitrary angles are obtained. The distinction between our method and that of H. Sagan is that we provide the generation process analytically and represent it as a graph of a series function which looks like the Weierstrass function. With these arithmetic expressions, we further analyze and prove some of the fractal properties of the Koch-type curves such as the self-similarity, the HSlder exponent and with the property of continuous everywhere but differentiable nowhere. Then, we will show that the Koch- type curves can be approximated by different constructed generators. Based on the analytic transformation of the Koch-type curves, we also constructed more continuous but nowhere-differentiable curves represented by arithmetic expressions. This result implies that the analytical expression of a fractal has theoretical and practical significance.
基金supported by National Natural Science Foundation of China (Grant No. 11601504)Fundamental Research Funds of the Central Universities (Grant No. DUT18RC(4)065)。
文摘In this paper, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a characterization of pseudo-periodic maps with nontrivial fractional Dehn twist coefficients. We also obtain some uniform lower bounds of non-zero fractional Dehn twist coefficients.
