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Multiplicity and Castelnuovo–Mumford Regularity of Stanley–Reisner Rings

Naoki Terai , icon-email Ken-ichi Yoshida

Abstract

In this paper, we pose the following conjecture and give a positive answer to the case dim⁡Δ≤2: Let Δ be a (d−1)-dimensional simplicial complex on [n]. Fix an integer ℓ with 0≤ℓ≤n−d−1. If e(K[Δ])≤(ℓ+1)d−ℓ and βℓ,ℓ+d(K[Δ])=0, then regK[Δ]≤d−1. \par Moreover, we discuss the relationship between the above conjecture and the lower bound theorem.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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