• 제목/요약/키워드: singular moduli

검색결과 15건 처리시간 0.026초

RECURSIONS FOR TRACES OF SINGULAR MODULI

  • Kim, Chang Heon
    • 충청수학회지
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    • 제21권2호
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    • pp.183-188
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    • 2008
  • We will derive recursion formulas satisfied by the traces of singular moduli for the higher level modular function.

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GENERATING FUNCTION OF TRACES OF SINGULAR MODULI

  • Kim, Chang Heon
    • 충청수학회지
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    • 제20권4호
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    • pp.375-386
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    • 2007
  • Let p be a prime and $f(z)=\Sigma_{n}a(n)q^n$ be a weakly holomorphic modular function for ${\Gamma}^*_0(p)$ with a(0) = 0. We use Bruinier and Funke's work to find the generating series of modular traces of f(z) as Jacobi forms.

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STALE REDUCTIONS OF SINGULAR PLANE QUARTICS

  • Kang, Pyung-Lyun
    • 대한수학회논문집
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    • 제9권4호
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    • pp.905-915
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    • 1994
  • Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

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COMPARISON OF TWO DESINGULARIZATIONS OF THE MODULI SPACE OF ELLIPTIC STABLE MAPS

  • Lho, Hyenho
    • 대한수학회지
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    • 제58권2호
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    • pp.501-523
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    • 2021
  • We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.

VANISHING THEOREM ON SINGULAR MODULI SPACES

  • Cho, Yong-Seung;Hong, Yoon-Hi
    • 대한수학회지
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    • 제33권4호
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    • pp.1069-1099
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    • 1996
  • Let X be a smooth, simply connected and oriented closed fourmanifold such that the dimension $b_{2}^{+}(X)$ of a maximal positive subspace for the intersection form is greater than or equal to 3.

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GEOMETRIC AND APPROXIMATION PROPERTIES OF GENERALIZED SINGULAR INTEGRALS IN THE UNIT DISK

  • Anastassiou George A.;Gal Sorin G.
    • 대한수학회지
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    • 제43권2호
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    • pp.425-443
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    • 2006
  • The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.

NONEXISTENCE OF A CREPANT RESOLUTION OF SOME MODULI SPACES OF SHEAVES ON A K3 SURFACE

  • Choy, Jae-Yoo;Kiem, Young-Hoon
    • 대한수학회지
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    • 제44권1호
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    • pp.35-54
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    • 2007
  • Let $M_c$ = M(2, 0, c) be the moduli space of O(l)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0\;and\;c_2=c$ on a K3 surface X, where O(1) is a generic ample line bundle on X. When $c=2n\geq4$ is even, $M_c$ is a singular projective variety equipped with a holomorphic symplectic structure on the smooth locus. In particular, $M_c$ has trivial canonical divisor. In [22], O'Grady asks if there is any symplectic desingularization of $M_{2n}$ for $n\geq3$. In this paper, we show that there is no crepant resolution of $M_{2n}$ for $n\geq3$. This obviously implies that there is no symplectic desingularization.

TWO ZAGIER-LIFTS

  • Kang, Soon-Yi
    • 충청수학회지
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    • 제30권2호
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    • pp.183-200
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    • 2017
  • Zagier lift gives a relation between weakly holomorphic modular functions and weakly holomorphic modular forms of weight 3/2. Duke and Jenkins extended Zagier-lifts for weakly holomorphic modular forms of negative-integral weights and recently Bringmann, Guerzhoy and Kane extended them further to certain harmonic weak Maass forms of negative-integral weights. New Zagier-lifts for harmonic weak Maass forms and their relation with Bringmann-Guerzhoy-Kane's lifts were discussed earlier. In this paper, we give explicit relations between the two different lifts via direct computation.

FORMULAS OF GALOIS ACTIONS OF SOME CLASS INVARIANTS OVER QUADRATIC NUMBER FIELDS WITH DISCRIMINANT D ≡ 1(mod 12)

  • Jeon, Daeyeol
    • 충청수학회지
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    • 제22권4호
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    • pp.799-814
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    • 2009
  • A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

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GALOIS ACTIONS OF A CLASS INVARIANT OVER QUADRATIC NUMBER FIELDS WITH DISCRIMINANT D≡64(mod72)

  • Jeon, Daeyeol
    • 충청수학회지
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    • 제26권1호
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    • pp.213-219
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    • 2013
  • A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.