Bounds for the cohomology and the Castelnuovo regularity of certain surfaces

Markus Brodmann, Wolfgang Vogel

Type: Article

Publication Date: 1993-09-01

Citations: 7

DOI: https://doi.org/10.1017/s0027763000004566

Abstract

Let X ⊆ P r be a reduced, irreducible and non-degenerate projective variety over an algebraically closed field K of characteristic 0. Let reg( x ) be the Castelnuovo-Mumford regularity of the sheaf of ideals associated to X . Then it is an open problem—due to D. Eisenbud (see e.g. [E-Go])—whether (0.1) reg( X ) ≤ deg( x ) - codim ( x ) + 1, where deg( x ) denotes the degree of X and codim( x ) denotes the codimension of X . In many cases, this inequality has been proven to hold true.

Locations

Nagoya Mathematical Journal - View - PDF
Project Euclid (Cornell University) - View - PDF
Zurich Open Repository and Archive (University of Zurich) - View - PDF

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+	Counterexamples to the Eisenbud–Goto regularity conjecture	2017	Jason McCullough Irena Peeva
+	Lectures on the Geometry of Syzygies	2004	David Eisenbud Jessica Sidman
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Works Cited by This (11)

Action	Title	Year	Authors
+	Sectional genus and cohomology of projective varieties	1991	Markus Brodmann
+	Castelnuovo bounds for certain subvarieties in ℙ n	1987	Jürgen Stückrad Wolfgang Vogel
+	On a theorem of Castelnuovo, and the equations defining space curves	1983	Laurent Gruson Robert Lazarsfeld Christian Peskine
+	Bounds on the cohomological Hilbert functions of a projective variety	1987	Markus Brodmann
+	Towards a structure theory for projective varieties of degree = codimension + 2	1991	Lê Tuâń Hoa Jürgen Stückrad Wolfgang Vogel
+	Local Cohomology Modules for Normal Domains	1979	E. Graham Evans Phillip Griffith
+	Castelnuovo-Mumford Regularity and Hyperplane Sections	1994	Lê Tuâń Hoa Wolfgang Vogel
+	Castelnuovo's regularity and cohomological properties of sets of points in ℙ n	1989	Jürgen Stückrad Wolfgang Vogel
+	A sharp Castelnuovo bound for smooth surfaces	1987	Robert Lazarsfeld
+ PDF Chat	A note on quasi-Buchsbaum rings	1984	Shirō Gotō