K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: The structure of the invariant
Yoshikawa in [Invent. Math. 156 (2004), 53–117] introduces a holomorphic torsion invariant of $K3$ surfaces with involution. In this paper we completely determine its structure as an automorphic function on the moduli space of such $K3$ surfaces. On every component of the moduli space, it is express...
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| Veröffentlicht in: | Compositio mathematica 2020-10, Vol.156 (10), p.1965-2019 |
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| container_end_page | 2019 |
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| container_start_page | 1965 |
| container_title | Compositio mathematica |
| container_volume | 156 |
| creator | Ma, Shouhei Yoshikawa, Ken-Ichi |
| description | Yoshikawa in [Invent. Math. 156 (2004), 53–117] introduces a holomorphic torsion invariant of $K3$ surfaces with involution. In this paper we completely determine its structure as an automorphic function on the moduli space of such $K3$ surfaces. On every component of the moduli space, it is expressed as the product of an explicit Borcherds lift and a classical Siegel modular form. We also introduce its twisted version. We prove its modularity and a certain uniqueness of the modular form corresponding to the twisted holomorphic torsion invariant. This is used to study an equivariant analogue of Borcherds’ conjecture. |
| doi_str_mv | 10.1112/S0010437X2000737X |
| format | Article |
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Math. 156 (2004), 53–117] introduces a holomorphic torsion invariant of $K3$ surfaces with involution. In this paper we completely determine its structure as an automorphic function on the moduli space of such $K3$ surfaces. On every component of the moduli space, it is expressed as the product of an explicit Borcherds lift and a classical Siegel modular form. We also introduce its twisted version. We prove its modularity and a certain uniqueness of the modular form corresponding to the twisted holomorphic torsion invariant. This is used to study an equivariant analogue of Borcherds’ conjecture.</abstract><cop>London, UK</cop><pub>London Mathematical Society</pub><doi>10.1112/S0010437X2000737X</doi><tpages>55</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Compositio mathematica, 2020-10, Vol.156 (10), p.1965-2019 |
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| language | eng |
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| source | Cambridge Journals Online; EZB Electronic Journals Library |
| subjects | Analytic functions Equality Invariants Mathematical analysis Modularity |
| title | K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: The structure of the invariant |
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