scholarly journals The Torelli map restricted to the hyperelliptic locus

2021 ◽  
Vol 8 (12) ◽  
pp. 354-378
Author(s):  
Aaron Landesman
Keyword(s):  
Hyperelliptic Locus

scholarly journals Modular forms vanishing on the hyperelliptic locus

2003 ◽  
Vol 29 (1) ◽  
pp. 135-142 ◽  
Author(s):  
Riccardo Salvati MANNI
Keyword(s):  
Modular Forms ◽  
Hyperelliptic Locus

scholarly journals Exceptional points in the elliptic–hyperelliptic locus

2008 ◽  
Vol 212 (6) ◽  
pp. 1415-1426 ◽  
Author(s):  
Ewa Tyszkowska ◽  
Anthony Weaver
Keyword(s):  
Exceptional Points ◽  
Hyperelliptic Locus

scholarly journals Dimensions of spaces of Siegel modular forms of low weight in degree four

1996 ◽  
Vol 54 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Cris Poor ◽  
David S. Yuen
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Geometric Methods ◽  
Low Weight ◽  
Hyperelliptic Locus

We calculate the dimensions of using Erokhin's work on Niemeier lattices and geometric methods involving the hyperelliptic locus.

scholarly journals On the dimension of voisin sets in the moduli space of abelian varieties

2021 ◽  
Author(s):  
E. Colombo ◽  
J. C. Naranjo ◽  
G. P. Pirola
Keyword(s):  
Abelian Variety ◽  
Moduli Space ◽  
Abelian Varieties ◽  
Chow Group ◽  
Hyperelliptic Locus

AbstractWe study the subsets $$V_k(A)$$ V k ( A ) of a complex abelian variety A consisting in the collection of points $$x\in A$$ x ∈ A such that the zero-cycle $$\{x\}-\{0_A\}$$ { x } - { 0 A } is k-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that $$\dim V_k(A) \le k-1$$ dim V k ( A ) ≤ k - 1 and $$\dim V_k(A)$$ dim V k ( A ) is countable for a very general abelian variety of dimension at least $$2k-1$$ 2 k - 1 . We study in particular the locus $${\mathcal {V}}_{g,2}$$ V g , 2 in the moduli space of abelian varieties of dimension g with a fixed polarization, where $$V_2(A)$$ V 2 ( A ) is positive dimensional. We prove that an irreducible subvariety $${\mathcal {Y}} \subset {\mathcal {V}}_{g,2}$$ Y ⊂ V g , 2 , $$g\ge 3$$ g ≥ 3 , such that for a very general $$y \in {\mathcal {Y}}$$ y ∈ Y there is a curve in $$V_2(A_y)$$ V 2 ( A y ) generating A satisfies $$\dim {\mathcal {Y}}\le 2g - 1.$$ dim Y ≤ 2 g - 1 . The hyperelliptic locus shows that this bound is sharp.

scholarly journals Concomitants of ternary quartics and vector-valued Siegel and Teichmüller modular forms of genus three

2020 ◽  
Vol 26 (4) ◽  
Author(s):  
Fabien Cléry ◽  
Carel Faber ◽  
Gerard van der Geer
Keyword(s):  
Representation Theory ◽  
Modular Form ◽  
Modular Forms ◽  
Siegel Modular Forms ◽  
Cusp Forms ◽  
Local Systems ◽  
Hyperelliptic Locus ◽  
Vector Valued

Abstract We show how one can use the representation theory of ternary quartics to construct all vector-valued Siegel modular forms and Teichmüller modular forms of degree 3. The relation between the order of vanishing of a concomitant on the locus of double conics and the order of vanishing of the corresponding modular form on the hyperelliptic locus plays an important role. We also determine the connection between Teichmüller cusp forms on $$\overline{\mathcal {M}}_{g}$$ M ¯ g and the middle cohomology of symplectic local systems on $${\mathcal {M}}_{g}\,$$ M g . In genus 3, we make this explicit in a large number of cases.

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