Pub Date : 2020-04-24DOI: 10.51286/albjm/1608313767
E. Ballico
Let $Wsubset mathbb {P}^n$, $nge 3$, be a degree $k$ hypersurface. Consider a "general" reducible, but connected, curve $Ysubset mathbb {P}^n$, for instance a sufficiently general connected and nodal union of lines with $p_a(Y)=0$, i.e. a tree of lines. We study the Hilbert function of the set $Ycap W$ with cardinality $k°(Y)$ and prove when it is the expected one. We give complete classification of the exceptions for $k=2$ and for $n=k=3$. We apply these results and tools to the case in which $Y$ is a smooth curve with $mathcal {O}_Y(1)$ non-special.
{"title":"On the Hilbert Function of Intersections of a Hypersurface with General Reducible Curves","authors":"E. Ballico","doi":"10.51286/albjm/1608313767","DOIUrl":"https://doi.org/10.51286/albjm/1608313767","url":null,"abstract":"Let $Wsubset mathbb {P}^n$, $nge 3$, be a degree $k$ hypersurface. Consider a \"general\" reducible, but connected, curve $Ysubset mathbb {P}^n$, for instance a sufficiently general connected and nodal union of lines with $p_a(Y)=0$, i.e. a tree of lines. We study the Hilbert function of the set $Ycap W$ with cardinality $k°(Y)$ and prove when it is the expected one. We give complete classification of the exceptions for $k=2$ and for $n=k=3$. We apply these results and tools to the case in which $Y$ is a smooth curve with $mathcal {O}_Y(1)$ non-special.","PeriodicalId":309211,"journal":{"name":"Albanian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122807779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-04DOI: 10.51286/albjm/1608313766
Neea Palojarvi
$tau$-Li coefficients describe if a function satisfies the Generalized Riemann Hypothesis or not. In this paper we prove that certain values of the $tau$-Li coefficients lead to existence or non-existence of certain zeros. The first main result gives explicit numbers $N_1$ and $N_2$ such that if all real parts of the $tau$-Li coefficients are non-negative for all indices between $N_1$ and $N_2$, then the function has non zeros outside a certain region. According to the second result, if some of the real parts of the $tau$-Li coefficients are negative for some index $n$ between numbers $n_1$ and $n_2$, then there is at least one zero outside a certain region.
{"title":"Explicit Zero-Free Regions and a $tau$-Li-type Criterion","authors":"Neea Palojarvi","doi":"10.51286/albjm/1608313766","DOIUrl":"https://doi.org/10.51286/albjm/1608313766","url":null,"abstract":"$tau$-Li coefficients describe if a function satisfies the Generalized Riemann Hypothesis or not. In this paper we prove that certain values of the $tau$-Li coefficients lead to existence or non-existence of certain zeros. The first main result gives explicit numbers $N_1$ and $N_2$ such that if all real parts of the $tau$-Li coefficients are non-negative for all indices between $N_1$ and $N_2$, then the function has non zeros outside a certain region. According to the second result, if some of the real parts of the $tau$-Li coefficients are negative for some index $n$ between numbers $n_1$ and $n_2$, then there is at least one zero outside a certain region.","PeriodicalId":309211,"journal":{"name":"Albanian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127422510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-10-19DOI: 10.51286/albjm/1693956885
D. Neftin, U. Vishne
A finite group G is admissible over a field M if there is a division algebra whose center is M with a maximal subfield G-Galois over M. We consider nine possible notions of being admissible over M with respect to a subfield K of M, where the division algebra, the maximal subfield or the Galois group are asserted to be defined over K. We completely determine the logical implications between all variants.
{"title":"FIELDS OF DEFINITION FOR ADMISSIBLE GROUPS","authors":"D. Neftin, U. Vishne","doi":"10.51286/albjm/1693956885","DOIUrl":"https://doi.org/10.51286/albjm/1693956885","url":null,"abstract":"A finite group G is admissible over a field M if there is a division algebra whose center is M with a maximal subfield G-Galois over M. We consider nine possible notions of being admissible over M with respect to a subfield K of M, where the division algebra, the maximal subfield or the Galois group are asserted to be defined over K. We completely determine the logical implications between all variants.","PeriodicalId":309211,"journal":{"name":"Albanian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122315498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.51286/albjm/1608313763
Hsian-Hua Tseng
{"title":"On Gromov-Witten Theory of Toric Gerbes","authors":"Hsian-Hua Tseng","doi":"10.51286/albjm/1608313763","DOIUrl":"https://doi.org/10.51286/albjm/1608313763","url":null,"abstract":"","PeriodicalId":309211,"journal":{"name":"Albanian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126886297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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