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Singular Yamabe problem for scalar flat metrics on the sphere 球面上标量平面度量的山边奇异问题
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-24 DOI: 10.1007/s00229-023-01527-x
Aram L. Karakhanyan
{"title":"Singular Yamabe problem for scalar flat metrics on the sphere","authors":"Aram L. Karakhanyan","doi":"10.1007/s00229-023-01527-x","DOIUrl":"https://doi.org/10.1007/s00229-023-01527-x","url":null,"abstract":"<p>Let <span>(Omega )</span> be a domain on the unit <i>n</i>-sphere <span>( {mathbb {S}}^n)</span> and <span>( overset{{,}_circ }{g})</span> the standard metric of <span>({mathbb {S}}^n)</span>, <span>(nge 3)</span>. We show that there exists a conformal metric <i>g</i> with vanishing scalar curvature <span>(R(g)=0)</span> such that <span>((Omega , g))</span> is complete if and only if the Bessel capacity <span>({mathcal {C}}_{alpha , q}({mathbb {S}}^nsetminus Omega )=0)</span>, where <span>(alpha =1+frac{2}{n})</span> and <span>(q=frac{n}{2})</span>. Our analysis utilizes some well known properties of capacity and Wolff potentials, as well as a version of the Hopf–Rinow theorem for the divergent curves.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds 四维凯勒流形上变形赫米蒂-杨-米尔斯度量的切尔数不等式
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-21 DOI: 10.1007/s00229-023-01531-1
Xiaoli Han, Xishen Jin
{"title":"Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds","authors":"Xiaoli Han, Xishen Jin","doi":"10.1007/s00229-023-01531-1","DOIUrl":"https://doi.org/10.1007/s00229-023-01531-1","url":null,"abstract":"<p>In this paper, we give an affirmative answer to a conjecture of Collins-Yau [8]. We investigate the Chern number inequalities on 4-dimensional Kähler manifolds admitting the deformed Hermitian-Yang-Mills metrics under the assumption <span>({{hat{theta }}}in (pi ,2pi ))</span>.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139508979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The string topology coproduct on complex and quaternionic projective space 复投影空间和四元投影空间上的弦拓扑共积
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-18 DOI: 10.1007/s00229-023-01532-0
Maximilian Stegemeyer
{"title":"The string topology coproduct on complex and quaternionic projective space","authors":"Maximilian Stegemeyer","doi":"10.1007/s00229-023-01532-0","DOIUrl":"https://doi.org/10.1007/s00229-023-01532-0","url":null,"abstract":"<p>On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the string topology coproduct on complex and quaternionic projective space. The behavior of the Goresky-Hingston product for these spaces then follows directly.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mass-growth of triangulated auto-equivalences 三角形自等式的质量增长
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-18 DOI: 10.1007/s00229-023-01533-z
Jon Woolf
{"title":"Mass-growth of triangulated auto-equivalences","authors":"Jon Woolf","doi":"10.1007/s00229-023-01533-z","DOIUrl":"https://doi.org/10.1007/s00229-023-01533-z","url":null,"abstract":"<p>We relate the mass growth (with respect to a stability condition) of an exact auto-equivalence of a triangulated category to the dynamical behaviour of its action on the space of stability conditions. One consequence is that this action is free and proper whenever the mass growth is non-vanishing.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weak Akizuki–Nakano vanishing theorem for singular globally F-split 3-folds 奇异全局 F 分裂 3 折叠的弱秋槻-中野消失定理
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-10 DOI: 10.1007/s00229-023-01529-9
Kenta Sato, Shunsuke Takagi
{"title":"Weak Akizuki–Nakano vanishing theorem for singular globally F-split 3-folds","authors":"Kenta Sato, Shunsuke Takagi","doi":"10.1007/s00229-023-01529-9","DOIUrl":"https://doi.org/10.1007/s00229-023-01529-9","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces 乌尔里希束的科斯祖尔特性和德尔佩佐曲面上稳定束的模空间合理性
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-09 DOI: 10.1007/s00229-023-01530-2
Purnaprajna Bangere, Jayan Mukherjee, Debaditya Raychaudhury
{"title":"Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces","authors":"Purnaprajna Bangere, Jayan Mukherjee, Debaditya Raychaudhury","doi":"10.1007/s00229-023-01530-2","DOIUrl":"https://doi.org/10.1007/s00229-023-01530-2","url":null,"abstract":"<p>Let <span>({mathscr {E}})</span> be a vector bundle on a smooth projective variety <span>(Xsubseteq {mathbb {P}}^N)</span> that is Ulrich with respect to the hyperplane section <i>H</i>. In this article, we study the Koszul property of <span>({mathscr {E}})</span>, the slope-semistability of the <i>k</i>-th iterated syzygy bundle <span>({mathscr {S}}_k({mathscr {E}}))</span> for all <span>(kge 0)</span> and rationality of moduli spaces of slope-stable bundles on Del Pezzo surfaces. As a consequence of our study, we show that if <i>X</i> is a Del Pezzo surface of degree <span>(dge 4)</span>, then any Ulrich bundle <span>({mathscr {E}})</span> satisfies the Koszul property and is slope-semistable. We also show that, for infinitely many Chern characters <span>(textbf{v}=(r,c_1, c_2))</span>, the corresponding moduli spaces of slope-stable bundles <span>({mathfrak {M}}_H(textbf{v}))</span> when non-empty, are rational, and thereby produce new evidences for a conjecture of Costa and Miró-Roig. As a consequence, we show that the iterated syzygy bundles of Ulrich bundles are dense in these moduli spaces.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139412916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterizations of Fano type varieties and projective spaces via absolute complexity 通过绝对复杂性确定法诺型变种和投影空间的特征
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-04 DOI: 10.1007/s00229-023-01526-y
Dae-Won Lee
{"title":"Characterizations of Fano type varieties and projective spaces via absolute complexity","authors":"Dae-Won Lee","doi":"10.1007/s00229-023-01526-y","DOIUrl":"https://doi.org/10.1007/s00229-023-01526-y","url":null,"abstract":"<p>In this paper, we obtain several characterizations of varieties of Fano type and projective spaces via absolute complexity. Also, we show that if the absolute complexity of a given pair <span>((X,Delta ))</span> is negative, then the pair <span>((X,Delta ))</span> does not admit any <span>(-(K_X+Delta ))</span>-minimal models.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gluing constructions for Lorentzian length spaces. 洛伦兹长度空间的胶合构造
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-01 Epub Date: 2023-03-24 DOI: 10.1007/s00229-023-01469-4
Tobias Beran, Felix Rott
{"title":"Gluing constructions for Lorentzian length spaces.","authors":"Tobias Beran, Felix Rott","doi":"10.1007/s00229-023-01469-4","DOIUrl":"10.1007/s00229-023-01469-4","url":null,"abstract":"<p><p>We introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out of old ones. The main application in this work is an analogue of the gluing theorem of Reshetnyak for CAT(<i>k</i>) spaces, which roughly states that gluing is compatible with upper curvature bounds. Due to the absence of a notion of spacelike distance in Lorentzian pre-length spaces we can only formulate the theorem in terms of (strongly causal) spacetimes viewed as Lorentzian length spaces.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10764570/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47325022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${overline{{{mathcal {M}}} }}_g$$ 模空间 $${overline{{mathcal {M}}} 上魏尔-彼得森度量的平均标量曲率估计值}}_g$$
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2023-12-10 DOI: 10.1007/s00229-023-01523-1
Georg Schumacher, Stefano Trapani
{"title":"Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${overline{{{mathcal {M}}} }}_g$$","authors":"Georg Schumacher, Stefano Trapani","doi":"10.1007/s00229-023-01523-1","DOIUrl":"https://doi.org/10.1007/s00229-023-01523-1","url":null,"abstract":"<p>We give a precise estimate for the average scalar curvature of the Weil–Petersson metric on the moduli space <span>({overline{{{mathcal {M}}} }}_g)</span> as <span>(grightarrow infty )</span> up to the order <span>(1/g^2)</span>.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138561539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zeta function of some Kummer Calabi-Yau 3-folds 一些库默尔 Calabi-Yau 3 折叠的 Zeta 函数
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2023-12-07 DOI: 10.1007/s00229-023-01524-0
Dominik Burek
{"title":"Zeta function of some Kummer Calabi-Yau 3-folds","authors":"Dominik Burek","doi":"10.1007/s00229-023-01524-0","DOIUrl":"https://doi.org/10.1007/s00229-023-01524-0","url":null,"abstract":"<p>We compute Hodge numbers and zeta function of a Kummer Calabi-Yau 3-folds introduced by M. Andreatta and J. Wiśniewski in [2] and investigated by M. Donten-Bury in [13].\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138546702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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