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Mario Maican

Publications and source records attributed to Mario Maican.

At least 19 recordsLinked to original sources
arXiv2024

The Relevant Domain of the Hilbert Function of a Finite Multiprojective Scheme

Let X be a zero-dimensional scheme contained in a multiprojective space. Let $s_i$ be the length of the projection of X onto the i-th component of the multiprojective space. A result of Van Tuyl states that the Hilbert function of X, in the case when X is reduced, is completely determined by its restriction to the product of the intervals $[0, s_i - 1]$. We prove that the same is also true for non-reduced schemes X.

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arXiv2021

Variation of moduli spaces of coherent systems of dimension one and order one

We study the wall-crossing for moduli spaces of coherent systems of dimension one and order one on a smooth projective variety over the complex numbers. We compute the topological Euler characteristic of the moduli spaces in the particular case when the variety is a quadric surface, the first Chern class of the coherent systems is of the form (2,r) and the second Chern class is bounded from below by 3r + 1 and also by 4r - 8.

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arXiv2021

The Effect on Topology of the Action of a Unipotent Group

Assume that two algebraic varieties of finite type over the complex numbers are related by a morphism whose fibers are precisely the orbits for the action of a unipotent group. We show that the two varieties have the same topological Euler characteristic. If they are smooth and the morphism is smooth, we show that the two varieties have the same cohomology groups.

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arXiv2019

Moduli of stable sheaves supported on curves of genus three contained in a quadric surface

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of alpha-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.

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arXiv2017

Moduli of space sheaves with Hilbert polynomial 4m+1

We investigate the moduli space of sheaves supported on space curves of degree 4 and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.

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arXiv2017

Moduli spaces of rank 2 instanton sheaves on the projective space

We study the irreducible components of the moduli space of instanton sheaves on $\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, we classify all instanton sheaves with $c_2(E)\le4$, describing all the irreducible components of their moduli space. A key ingredient for our argument is the study of the moduli space ${\mathcal T}(d)$ of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $P(t)=d\cdot t$, which contains, as an open subset, the moduli space of rank 0 instanton sheaves of multiplicity $d$; we describe all the irreducible components of ${\mathcal T}(d)$ for $d\le4$.

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arXiv2017

Moduli of sheaves supported on curves of genus two in a quadric surface

We study the moduli space of stable sheaves of Euler characteristic 1, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We give a classification of the stable sheaves involving locally free resolutions or extensions. We compute the Betti numbers by studying the variation of the moduli spaces of alpha-semi-stable pairs.

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arXiv2015

Moduli of sheaves supported on quartic space curves

As a continuation of the work of Freiermuth and Trautmann, we study the geometry of the moduli space of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $4m+1$. The moduli space has three irreducible components whose generic elements are, respectively, sheaves supported on rational quartic curves, on elliptic quartic curves, or on planar quartic curves. The main idea of the proof is to relate the moduli space with the Hilbert scheme of curves by wall crossing. We present all stable sheaves contained in the intersections of the three irreducible components. We also classify stable sheaves by means of their free resolutions.

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arXiv2015

On two moduli spaces of sheaves supported on quadric surfaces

We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension 1, multiplicity 4, Euler characteristic 2, and first Chern class (2, 2), is the blow-up at two points of a certain hypersurface in a weighted projective space.

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arXiv2013

The homology groups of certain moduli spaces of plane sheaves

Using the Bialynicki-Birula method, we determine the additive structure of the integral homology groups of the moduli spaces of semi-stable sheaves on the projective plane having rank and Chern classes (5, 1, 4), (7, 2, 6), respectively, (0, 5, 19). We compute the Hodge numbers of these moduli spaces.

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arXiv2013

Torus action on the moduli spaces of plane sheaves

We describe the torus fixed locus of the moduli space of stable sheaves with Hilbert polynomial $4m+1$ on the projective plane. We determine the torus representation of the tangent spaces at the fixed points, which leads to the computation of the Betti and Hodge numbers of the moduli space.

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arXiv2012

The classification of semi-stable plane sheaves supported on sextic curves

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients modulo actions of certain algebraic groups. In most cases we give concrete geometric descriptions of the strata.

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arXiv2012

On the moduli spaces of semi-stable plane sheaves of dimension one and multiplicity five

We find locally free resolutions of length one for all semi-stable sheaves supported on curves of multiplicity five in the complex projective plane. In some cases we also find geometric descriptions of these sheaves by means of extensions. We give natural stratifications for their moduli spaces and we describe the strata as certain quotients modulo linear algebraic groups. In most cases we give concrete descriptions of these quotients as fibre bundles.

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