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We give a formula that relates the difference of the j-invariants with the Borcherds Phi-function, an automorphic form on the period domain for Enriques surfaces characterizing the discriminant divisor.
Comment: Section 8 added, references updat
Comment: Section 8 added, references updat
Externí odkaz:
http://arxiv.org/abs/2103.02540
Autor:
Hsia, Liang-Chung, Kawaguchi, Shu
In this paper we study arithmetic properties of a one-parameter family ${\mathbf H}$ of H\'enon maps over the affine line. Given a family of initial points ${\mathbf P}$ satisfying a natural condition, we show the height function $h_{{\mathbf P}}$ as
Externí odkaz:
http://arxiv.org/abs/1810.03841
Autor:
Kawaguchi, Shu, Yamaki, Kazuhiko
Let $R$ be a complete discrete valuation ring of equi-characteristic zero with fractional field $K$. Let $X$ be a connected, smooth projective variety of dimension $d$ over $K$, and let $L$ be an ample line bundle over $X$. We assume that there exist
Externí odkaz:
http://arxiv.org/abs/1612.01099
Autor:
Kawaguchi, Shu, Yamaki, Kazuhiko
For a connected smooth projective curve $X$ of genus $g$, global sections of any line bundle $L$ with $\deg(L) \geq 2g+ 1$ give an embedding of the curve into projective space. We consider an analogous statement for a Berkovich skeleton in nonarchime
Externí odkaz:
http://arxiv.org/abs/1612.01098
Autor:
Kawaguchi, Shu, Yamaki, Kazuhiko
Publikováno v:
Kyoto J. Math. 56, no. 1 (2016), 177-196
Let $\bar{G} = (G, \omega)$ be a vertex-weighted graph, and $\delta$ a divisor class on $G$. Let $r_{\bar{G}}(\delta)$ denote the combinatorial rank of $\delta$. Caporaso has introduced the algebraic rank $r_{\bar{G}}^{\operatorname{alg}}(\delta)$ of
Externí odkaz:
http://arxiv.org/abs/1401.3935
Publikováno v:
American Journal of Mathematics, 2018 Dec 01. 140(6), 1471-1519.
Externí odkaz:
https://www.jstor.org/stable/26979616
Autor:
Kawaguchi, Shu
Kyoto University (京都大学)
0048
甲第7936号
理博第2102号
新制||理||1122(附属図書館)
UT51-99-M241
学位規則第4条第1項該当
0048
甲第7936号
理博第2102号
新制||理||1122(附属図書館)
UT51-99-M241
学位規則第4条第1項該当
Externí odkaz:
http://hdl.handle.net/2433/181423
The Borcherds Phi-function is the automorphic form on the moduli space of Enriques surfaces characterizing the discriminant locus. In this paper, we give an algebro-geometric construction of the Borcherds Phi-function.
Externí odkaz:
http://arxiv.org/abs/1308.6454
Publikováno v:
Bull Inst. Math. Academia Sinica 9 (2014), 547-584
The classical (m,k)-Landen transform F_{m,k} is a self-map of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m'th roots of unity. Identifying the set of rational maps of degree d with
Externí odkaz:
http://arxiv.org/abs/1308.5355
Autor:
Kawaguchi, Shu, Yamaki, Kazuhiko
Publikováno v:
Int. Math. Res. Not. 2015, no. 12, 4121--4176
Let $(G, \omega)$ be a hyperelliptic vertex-weighted graph of genus $g \geq 2$. We give a characterization of $(G, \omega)$ for which there exists a smooth projective curve $X$ of genus $g$ over a complete discrete valuation field with reduction grap
Externí odkaz:
http://arxiv.org/abs/1304.6979