Ulrich sheaves and higher-rank Brill-Noether theory

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• 作者：Rajesh S. Kulkarni^a ; ^{kulkarni@math.msu.edu} ; Yusuf Mustopa^b ; ^{Yusuf.Mustopa@tufts.edu} ; Ian Shipman^c ; ^{shipman@math.utah.edu}
• 关键词：Ulrich bundles ; Brill&ndash ; Noether theory
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：474
• 期：Complete
• 页码：166-179
• 全文大小：371 K
• 卷排序：474

文摘

We show that the existence of an Ulrich sheaf on a projective variety X⊆PNX⊆PN is equivalent to the solution of a (possibly) higher-rank Brill–Noether problem for a curve on X that is rarely general in moduli. In addition, we exhibit a large family of curves for which this Brill–Noether problem admits a solution, and we show that existence of an Ulrich sheaf for a finite morphism of smooth projective varieties of any dimension implies sharp numerical constraints involving the degree of the map and the ramification divisor.