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Masaaki Murakami

Publications and source records attributed to Masaaki Murakami.

5 recordsLinked to original sources
arXiv2020

Surfaces with $c_1^2 =9$ and $χ=5$ whose canonical classes are divisible by $3$

We shall study minimal complex surfaces with $c^2 = 9$ and $χ=5$ whose canonical classes are divisible by $3$ in the integral cohomology groups, where $c_1^2$ and $χ$ denote the first Chern number of an algebraic surface and the Euler characteristic of the structure sheaf, respectively. The main results are a structure theorem for such surfaces, the unirationality of the moduli space, and a description of the behavior of the canonical map. As a byproduct, we shall also rule out a certain case mentioned in a paper by Ciliberto--Francia--Mendes Lopes. Since the irregularity $q$ vanishes for our surfaces, our surfaces have geometric genus $p_g = 4$.

math.AG↗
arXiv2013

Notes on hyperelliptic fibrations of genus 3, II

This is the part II of the series under the same title. In part I, using the approach developed by Catanese--Pignatelli arXiv:math/0503294, we gave a structure theorem for hyperelliptic genus 3 fibrations all of whose fibers are 2-connected (arXiv:1209.6278 [math.AG]). In this part II, we shall give a structure theorem for smooth deformation families of these to non-hyperelliptic genus 3 fibrations. As an application, we shall give a set of sufficient conditions for our genus 3 hyperelliptic fibration above to allow deformation to non-hyperelliptic fibrations, and use this to study certain minimal regular surfaces with first Chern number 8 and geometric genus 4: we shall find in the moduli space two strata M_0^{sharp} and M_0^{flat}$ (each of dimensions 32 and 30, respectively), and show that Bauer--Pingatelli's stratum M_0 (arXiv:math/0603094) and its 26-dimensional substratum are at the boundary of these new strata M_0^{sharp} and M_0^{flat}, respectively.

math.AG↗
arXiv2012

Remarks on surfaces with $c_1^2 = 2χ-1$ having non-trivial 2-torsion

We shall show that any complex minimal surface of general type with c_1^2 = 2χ-1 having non-trivial 2-torsion divisors, where c_1^2 and χare the first Chern number of a surface and the Euler characteristic of the structure sheaf respectively, has the Euler characteristic χnot exceeding 4. Moreover, we shall give a complete description for the surfaces of the case χ=4, and prove that the coarse moduli space for surfaces of this case is a unirational variety of dimension 29. Using the description, we shall also prove that our surfaces of the case χ= 4 have non-birational bicanonical maps and no pencil of curves of genus 2, hence being of so called non-standard case for the non-birationality of the bicanonical maps.

math.AG↗
arXiv2012

Notes on hyperelliptic fibrations of genus 3, I

We shall study the structure of hyperelliptic fibrations of genus 3, from the view point given by Catanese and Pignatelli in arXiv:math/0503294. In this part I, we shall give a structure theorem for such fibrations for the case of f : S \to B with all fibers 2-connected. We shall also give, for the case of B projective line, sufficient conditions for the existence of such fibrations from the view point of our structure theorem, prove the uniqueness of the deformation type and the simply connectedness of S for some cases, and give some examples including those with minimal regular S with geometric genus 4 and the first Chern number 8. The last example turns out to be a member of the family M_0 given in Bauer--Pignatelli arXiv:math/0603094.

math.AG↗