Projective varieties of maximal sectional regularity

详细信息    查看全文

• 作者：Markus Brodmann^a ; ^{brodmann@math.unizh.ch" class="auth_mail" title="E-mail the corresponding author} ; Wanseok Lee^b ; ^{wslee@pknu.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Euisung Park^c ; ^{euisungpark@korea.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Peter Schenzel^d ; ^{schenzel@informatik.uni-halle.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 14H45 ; 13D02
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：221
• 期：1
• 页码：98-118
• 全文大小：497 K

文摘

We study projective varieties athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si1.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=186d04a5acf9b344946e8eb1136d79ac" title="Click to view the MathML source">X⊂P^rathContainer hidden">athCode">ath altimg="si1.gif" overflow="scroll">X⊂athvariant="double-struck">Prath> of dimension athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si2.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=51156c24f315c0add5994880b6edbf29" title="Click to view the MathML source">n≥2athContainer hidden">athCode">ath altimg="si2.gif" overflow="scroll">n≥2ath>, of codimension athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si169.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=c77a2bbee5b37acdc8f4d76dc650fb71" title="Click to view the MathML source">c≥3athContainer hidden">athCode">ath altimg="si169.gif" overflow="scroll">c≥3ath> and of degree athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si170.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=17f3e2590299327222b84f503ee74558" title="Click to view the MathML source">d≥c+3athContainer hidden">athCode">ath altimg="si170.gif" overflow="scroll">d≥c+3ath> that are of maximal sectional regularity, i.e. varieties for which the Castelnuovo–Mumford regularity athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si5.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=fdc2bb7cb5b20b45e03a8358541ba191" title="Click to view the MathML source">reg(C)athContainer hidden">athCode">ath altimg="si5.gif" overflow="scroll">athvariant="normal">reg(athvariant="script">C)ath> of a general linear curve section is equal to athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si569.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=bc79c278c419d1f3f769823959eb4cc4" title="Click to view the MathML source">d−c+1athContainer hidden">athCode">ath altimg="si569.gif" overflow="scroll">d−c+1ath>, the maximal possible value (see [10]). As one of the main results we classify all varieties of maximal sectional regularity. If X   is a variety of maximal sectional regularity, then either (a) it is a divisor on a rational normal athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si572.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=521f634294f30d92729addce6d58e915" title="Click to view the MathML source">(n+1)athContainer hidden">athCode">ath altimg="si572.gif" overflow="scroll">(n+1)ath>-fold scroll athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si8.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=d99e6818d34824aca25f3d06da1a85f7" title="Click to view the MathML source">Y⊂Pⁿ⁺³athContainer hidden">athCode">ath altimg="si8.gif" overflow="scroll">Y⊂athvariant="double-struck">Pn+3ath> or else (b) there is an n  -dimensional linear subspace athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si290.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=e9134c536eb2702627e07ee91e9be614" title="Click to view the MathML source">F⊂P^rathContainer hidden">athCode">ath altimg="si290.gif" overflow="scroll">athvariant="double-struck">F⊂athvariant="double-struck">Prath> such that athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si10.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=bcd014f8fdfc4d09443ae53fef6da26e" title="Click to view the MathML source">X∩F⊂FathContainer hidden">athCode">ath altimg="si10.gif" overflow="scroll">X∩athvariant="double-struck">F⊂athvariant="double-struck">Fath> is a hypersurface of degree athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si569.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=bc79c278c419d1f3f769823959eb4cc4" title="Click to view the MathML source">d−c+1athContainer hidden">athCode">ath altimg="si569.gif" overflow="scroll">d−c+1ath>. Moreover, suppose that athmlsrc">atext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300706&_mathId=si11.gif&_user=111111111&_pii=S0022404916300706&_rdoc=1&_issn=00224049&md5=d3013ed5eae3a77fc375f40bb2a56107" title="Click to view the MathML source">n=2athContainer hidden">athCode">ath altimg="si11.gif" overflow="scroll">n=2ath> or the characteristic of the ground field is zero. Then in case (b) we obtain a precise description of X as a birational linear projection of a rational normal n-fold scroll.