

Publications 

[16]

M. Halic,
Semistable vector bundles on fibred varieties. Eur. J. Math. (accepted).
We introduce and investigate a semistability concept relative to morphisms π:Y→X between projective manifolds,
different of MaruyamaSimpson. For torsionfree sheaves on Y and appropriate polarizations, we relate the (semi)stability
on Y to the slope (semi)stability along the generic fibre of π.
We apply the result to describe in detail the moduli spaces of semistable vector bundles on Hirzebruch surfaces
and on threefolds which are P^{2}bundles over P^{1}. We establish their irreducibility and rationality,
an intensely investigated issue.


[15]

M. Halic,
Splitting criteria for vector bundles induced by restrictions to divisors.
Michigan Math. J. 68 (2018).
Inhere we obtain splitting and triviality criteria for vector bundles by restricting them to partially
positive divisors. In particular, we deduce an algorithmic method to check the splitting of vector bundles
on products of minuscule rational homogeneous varieties; no similar criterion was known even for a product
of two Grassmannians.


[14]

M. Halic,
Restriction properties for the KrullSchmidt decomposition of vector bundles. Internat. J. Math. 29 (2018).
We compare the KrullSchmidt decompositions of a vector bundle on a projective variety and that of its restriction to an ample subvariety.
The main result is a general Horrockstype criterion for KrullSchmidt decompositions. Finally, we obtain a simple splitting criterion for
vector bundles on partial flag varieties.


[13]

M. Halic, R. Tajarod,
About the cohomological dimension of certain stratified varieties.
Proc. Amer. Math. Soc. 145 (2017), 5157  5167.
We determine an upper bound for the cohomological dimension of the complement of
a closed subset in a projective variety which possesses an appropriate stratification.
We apply the result to several particular cases, including the BialynickiBirula
stratification; in this latter case, the bound is optimal.


[12]

M. Halic,
Splitting criteria for vector bundles on minuscule homogeneous varieties.
Transform. Groups 22 (2017), 753  765.
A vector bundle on a minuscule homogeneous variety splits
into a direct sum of line bundles if and only if its restriction to
the union of the twodimensional Schubert subvarieties splits.
The result is illustrated with examples.


[11]

M. Halic, R. Tajarod,
On the qampleness of the tensor product of two line bundles.
manuscripta math. 151 (2016), 177  182.
The tensor product of two line bundles, one being qample and the other
with sufficiently lowdimensional stable base locus, is still qample.


[10]

M. Halic,
Erratum to: Modular properties of nodal curves on K3 surfaces.
Math. Z. 280 (2015), 1203  1211.
I correct an error in [8] and I also obtain a lower bound
for the multiple Seshadri constants of general K3 surfaces.


[9]

M. Halic, R.Tajarod,
A cohomological splitting criterion for locally free sheaves
on arithmetically CohenMacaulay surfaces.
Math. Proc. Cambridge Philos. Soc. 155 (2013), 517  527.


[8]

M. Halic,
Modular properties of nodal curves on K3 surfaces.
Math. Z. 270 (2012), 871  887.


[7]

M. Halic,
Cohomological properties of invariant quotients of affine spaces.
J. London Math. Soc. 82 (2010), 376  394.


[6]

M. Halic,
A remark about the rigidity of curves on K3 surfaces.
Collectanea Math. 61 (2010), 323  336.


[5]

M. Halic,
Gauge theoretical/Hamiltonian GromovWitten invariants of toric varieties.
Math. Z. 252 (2006), 157  208.


[4]

M. Halic, S. Stupariu,
Rings of invariants for representations of quivers.
C.R. Acad. Sci. Paris 340 (2005), 135  140.


[3]

M. Halic,
Families of toric varieties.
Math. Nachr. 261262 (2003), 60  84.


[2]

M. Halic,
GW invariants and invariant quotients.
Comment. Math. Helv. 77 (2002), 145  191.


[1]

M. Halic,
On the geography of symplectic 6manifolds.
manuscripta math. 99 (1999), 371  381.


[0]

Ph.D. thesis
''Symplectique vs Projectif''.
