{"title":"The Dirichlet problem for prescribed curvature equations of p-convex hypersurfaces","authors":"Weisong Dong","doi":"10.1007/s00229-023-01522-2","DOIUrl":"https://doi.org/10.1007/s00229-023-01522-2","url":null,"abstract":"<p>In this paper, we study the Dirichlet problem for <i>p</i>-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"18 5-6","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512722","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}
{"title":"Polyharmonic surfaces in 3-dimensional homogeneous spaces","authors":"S. Montaldo, C. Oniciuc, A. Ratto","doi":"10.1007/s00229-023-01520-4","DOIUrl":"https://doi.org/10.1007/s00229-023-01520-4","url":null,"abstract":"Abstract In the first part of this paper we shall classify proper triharmonic isoparametric surfaces in 3-dimensional homogeneous spaces (Bianchi-Cartan-Vranceanu spaces, shortly BCV-spaces). We shall also prove that triharmonic Hopf cylinders are necessarily CMC. In the last section we shall determine a complete classification of CMC r -harmonic Hopf cylinders in BCV-spaces, $$r ge 3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . This result ensures the existence, for suitable values of r , of an ample family of new examples of r -harmonic surfaces in BCV-spaces.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"39 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136281667","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}
{"title":"Cuspidal components of Siegel modular forms for large discrete series representations of $$textrm{Sp}_4({mathbb {R}})$$","authors":"Shuji Horinaga, Hiro-aki Narita","doi":"10.1007/s00229-023-01513-3","DOIUrl":"https://doi.org/10.1007/s00229-023-01513-3","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"64 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136282312","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}
{"title":"Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances","authors":"Guanhua Liu","doi":"10.1007/s00229-023-01521-3","DOIUrl":"https://doi.org/10.1007/s00229-023-01521-3","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":" 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241329","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}
{"title":"On algebraic Chern classes of flat vector bundles","authors":"Adrian Langer","doi":"10.1007/s00229-023-01518-y","DOIUrl":"https://doi.org/10.1007/s00229-023-01518-y","url":null,"abstract":"Abstract We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Bloch’s conjecture on Chern classes of flat vector bundles on smooth complex projective varieties but in some cases they give a more precise information. We also study Higgs version of Bloch’s conjecture and analogous problems in the positive characteristic case.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":" 90","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191536","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}
{"title":"On the rationality of certain Fano threefolds","authors":"Ciro Ciliberto","doi":"10.1007/s00229-023-01514-2","DOIUrl":"https://doi.org/10.1007/s00229-023-01514-2","url":null,"abstract":"Abstract In this paper we study the rationality problem for Fano threefolds $$Xsubset {mathbb P}^{p+1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> of genus p , that are Gorenstein, with at most canonical singularities. The main results are: (1) a trigonal Fano threefold of genus p is rational as soon as $$pgeqslant 8$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> (this result has already been obtained in Przyjalkowski et al. (Izv Math 69(2):365–421, 2005), but we give here an independent proof); (2) a non-trigonal Fano threefold of genus $$pgeqslant 7$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> containing a plane is rational; (3) any Fano threefold of genus $$pgeqslant 17$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> </mml:math> is rational; (4) a Fano threefold of genus $$pgeqslant 12$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:math> containing an ordinary line $$ell $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ℓ</mml:mi> </mml:math> in its smooth locus is rational.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"32 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135584251","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}
{"title":"Boundedness of regular del Pezzo surfaces over imperfect fields","authors":"Hiromu Tanaka","doi":"10.1007/s00229-023-01517-z","DOIUrl":"https://doi.org/10.1007/s00229-023-01517-z","url":null,"abstract":"Abstract For a regular del Pezzo surface X , we prove that $$|-12K_X|$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>-</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> is very ample. Furthermore, we also give an explicit upper bound for the volume $$K_X^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mi>X</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> which depends only on $$[k: k^p]$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>:</mml:mo> <mml:msup> <mml:mi>k</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> for the base field k . As a consequence, we obtain the boundedness of geometrically integral regular del Pezzo surfaces.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136067570","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}
{"title":"Bounds for GL$$_2$$ $$times $$ GL$$_2$$ L-functions in the depth aspect","authors":"Qingfeng Sun","doi":"10.1007/s00229-023-01515-1","DOIUrl":"https://doi.org/10.1007/s00229-023-01515-1","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"30 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136232794","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}
{"title":"On classic n-universal quadratic forms over dyadic local fields","authors":"Zilong He","doi":"10.1007/s00229-023-01516-0","DOIUrl":"https://doi.org/10.1007/s00229-023-01516-0","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"46 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135316036","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}