Markus Brodmann
University of Zuerich, Switzerland
July 7, 2016
Projective Varieties of Maximal Sectional Regularity: We give a survey on joint work with Wanseok Lee, Euisung Park and Peter Schenzel. By Gruson-Peskine-Lazarsfeld, projective curves of maximal (Castelnuovo-Mumford) regularity were classified. Our aim is, to extend this classification to projective varieties of higher dimension. We therefore study $n$-dimensional irreducible non-degenerate projective varieties $X \subset \mathbb{P}^r$ with the property that for a general linear subspace $\mathbb{L} \in \mathbb{G}(r-n+1, \mathbb{P}^r)$ of $\mathbb{P}^r$ with dimension $r-n+1$ the intersection $X \cap \mathbb{L} \subset \mathbb{L}$ is a curve of maximal regularity. We classify such varieties and describe their geometric, homological and cohomological properties. We also mention a few open problems concerning our subject.
University of Zuerich, Switzerland
July 7, 2016
Projective Varieties of Maximal Sectional Regularity: We give a survey on joint work with Wanseok Lee, Euisung Park and Peter Schenzel. By Gruson-Peskine-Lazarsfeld, projective curves of maximal (Castelnuovo-Mumford) regularity were classified. Our aim is, to extend this classification to projective varieties of higher dimension. We therefore study $n$-dimensional irreducible non-degenerate projective varieties $X \subset \mathbb{P}^r$ with the property that for a general linear subspace $\mathbb{L} \in \mathbb{G}(r-n+1, \mathbb{P}^r)$ of $\mathbb{P}^r$ with dimension $r-n+1$ the intersection $X \cap \mathbb{L} \subset \mathbb{L}$ is a curve of maximal regularity. We classify such varieties and describe their geometric, homological and cohomological properties. We also mention a few open problems concerning our subject.