Pre-Tango structures and uniruled varieties

• Autorzy: Yoshifumi Takeda
• Języki publikacji: EN

Abstrakty

EN

The pre-Tango structure is an ample invertible sheaf of locally exact differentials on a variety of positive characteristic. It is well known that pre-Tango structures on curves often induce pathological uniruled surfaces. We show that almost all pre-Tango structures on varieties induce higher-dimensional pathological uniruled varieties, and that each of these uniruled varieties also has a pre-Tango structure. For this purpose, we first consider the p-closed rational vector field induced by a pre-Tango structure, and the smoothness of the fibration induced by the p-closed rational vector field.
Moreover, we give two examples: of a 3-dimensional variety of general type whose automorphism group scheme is not reduced, and of a non-uniruled variety which has a pre-Tango structure inducing a higher-dimensional pathological uniruled variety.

Kategorie tematyczne

• 14J29: Surfaces of general type
• 14J50: Automorphisms of surfaces and higher-dimensional varieties
• 14F17: Vanishing theorems
• 14F40: de Rham cohomology
• 14F05: Sheaves, derived categories of sheaves and related constructions
• 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli
• 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
• 14D06: Fibrations, degenerations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 2
• Strony: 193-216

Daty

wydano

2007

Twórcy

autor

Yoshifumi Takeda

• Department of Mathematics, Nara Women's University, Nara 6308506, Japan

Identyfikatory

DOI

10.4064/cm108-2-4