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On surfaces of general type with pg = q = 1, K2 = 3.

Francesco Polizzi (2005)

Collectanea Mathematica

The moduli space M of surfaces of general type with pg = q = 1, K2 = g = 3 (where g is the genus of the Albanese fibration) was constructed by Catanese and Ciliberto in [14]. In this paper we characterize the subvariety M2 ⊂ M corresponding to surfaces containing a genus 2 pencil, and moreover we show that there exists a non-empty, dense subset M0 ⊂ M which parametrizes isomorphism classes of surfaces with birational bicanonical map.

On surfaces with p 𝑔 = q = 1 and non-ruled bicanonical involution

Carlos Rito (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

This paper classifies surfaces S of general type with p g = q = 1 having an involution i such that S / i has non-negative Kodaira dimension and that the bicanonical map of S factors through the double cover induced by i . It is shown that S / i is regular and either: a) the Albanese fibration of S is of genus 2 or b) S has no genus 2 fibration and S / i is birational to a K 3 surface. For case a) a list of possibilities and examples are given. An example for case b) with K 2 = 6 is also constructed.

On the automorphisms of surfaces of general type in positive characteristic

Edoardo Ballico (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Here we give an explicit polynomial bound (in term of K X 2 and not depending on the prime p ) for the order of the automorphism group of a minimal surface X of general type defined over a field of characteristic p > 0 .

On the automorphisms of surfaces of general type in positive characteristic, II

Edoardo Ballico (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Here we give an upper polynomial bound (as function of K X 2 but independent on p ) for the order of a p -subgroup of A ⁢ u ⁢ t ⁢ X r ⁢ e ⁢ d with X minimal surface of general type defined over the field K with c ⁢ h ⁢ a ⁢ r ⁢ K = p > 0 . Then we discuss the non existence of similar bounds for the dimension as K -vector space of the structural sheaf of the scheme A ⁢ u ⁢ t ⁢ X .

Pre-Tango structures and uniruled varieties

Yoshifumi Takeda (2007)

Colloquium Mathematicae

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...

Currently displaying 41 – 60 of 73