کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665538 | 1633816 | 2015 | 76 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Framed sheaves on projective stacks
ترجمه فارسی عنوان
شبیه سازی فریم در پشته های تصویری
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
Given a normal projective irreducible stack X over an algebraically closed field of characteristic zero we consider framed sheaves on X, i.e., pairs (E,ÏE), where E is a coherent sheaf on X and ÏE is a morphism from E to a fixed coherent sheaf F. After introducing a suitable notion of (semi)stability, we construct a projective scheme, which is a moduli space for semistable framed sheaves with fixed Hilbert polynomial, and an open subset of it, which is a fine moduli space for stable framed sheaves. If X is a projective irreducible orbifold of dimension two and F a locally free sheaf on a smooth divisor DâX satisfying certain conditions, we consider (D,F)-framed sheaves, i.e., framed sheaves (E,ÏE) with E a torsion-free sheaf which is locally free in a neighbourhood of D, and ÏE|D an isomorphism. These pairs are μ-stable for a suitable choice of a parameter entering the (semi)stability condition, and of the polarization of X. This implies the existence of a fine moduli space parameterizing isomorphism classes of (D,F)-framed sheaves on X with fixed Hilbert polynomial, which is a quasi-projective scheme. In an appendix we develop the example of stacky Hirzebruch surfaces. This is the first paper of a project aimed to provide an algebro-geometric approach to the study of gauge theories on a wide class of 4-dimensional Riemannian manifolds by means of framed sheaves on “stacky” compactifications of them. In particular, in a subsequent paper [20] these results are used to study gauge theories on ALE spaces of type Ak.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 272, 26 February 2015, Pages 20-95
Journal: Advances in Mathematics - Volume 272, 26 February 2015, Pages 20-95
نویسندگان
Ugo Bruzzo, Francesco Sala, Mattia Pedrini,