Search results for: Justyna Szpond

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article

Unexpected curves and Togliatti‐type surfaces

Justyna Szpond

Mathematische Nachrichten > 293 > 1 > 158 - 168

The purpose of this note is to establish a direct link between the theory of unexpected hypersurfaces and varieties with defective osculating behavior. We identify unexpected plane curves of degree 4 as sections of a rational surface

X_{B}

of degree 7 in

P^{5}

with its osculating spaces of order 2 which in every point of

X_{B}

have dimension lower than expected. We put this result in perspective with earlier...

article

Lower Bounds for Waldschmidt Constants of Generic Lines in $${\mathbb {P}}^3$$ P3 and a Chudnovsky-Type Theorem

Marcin Dumnicki, Mohammad Zaman Fashami, Justyna Szpond, Halszka Tutaj-Gasińska

Mediterranean Journal of Mathematics > 2019 > 16 > 2 > 1-15

The Waldschmidt constant $${{\,\mathrm{{\widehat{\alpha }}}\,}}(I)$$ α^(I) of a radical ideal I in the coordinate ring of $${\mathbb {P}}^N$$ PN measures (asymptotically) the degree of a hypersurface passing through the set defined by I in $${\mathbb {P}}^N$$ PN . Nagata’s approach to the 14th Hilbert Problem was based on computing such constant for the set of points in $${\mathbb {P}}^2$$ P2 ....

article

From Pappus Theorem to parameter spaces of some extremal line point configurations and applications

Magdalena Lampa-Baczyńska, Justyna Szpond

Geometriae Dedicata > 2017 > 188 > 1 > 103-121

In the present work we study parameter spaces of two line point configurations introduced by Böröczky. These configurations are extremal from the point of view of the Dirac–Motzkin Conjecture settled recently by Green and Tao (Discrete Comput Geom 50:409–468, 2013). They have appeared also recently in commutative algebra in connection with the containment problem for symbolic and ordinary powers of...

article

Asymptotic Hilbert polynomials and limiting shapes

Marcin Dumnicki, Justyna Szpond, Halszka Tutaj-Gasińska

Journal of Pure and Applied Algebra > 2015 > 219 > 10 > 4446-4457

The main aim of this paper is to provide a method which allows finding limiting shapes of symbolic generic initial systems of higher-dimensional subvarieties of Pn. M. Mustaţă and S. Mayes established a connection between volumes of complements of limiting shapes and the asymptotic multiplicity for ideals of points. In the paper we prove a generalization of this fact to higher-dimensional sets.

article

Points fattening on P1×P1 and symbolic powers of bi-homogeneous ideals

Magdalena Baczyńska, Marcin Dumnicki, Agata Habura, Grzegorz Malara, more

Journal of Pure and Applied Algebra > 2014 > 218 > 8 > 1555-1562

We study symbolic powers of bi-homogeneous ideals of points in X=P1×P1 and extend to this setting results on the effect of points fattening obtained in [2] and [4]. We prove a Chudnovsky-type theorem for bi-homogeneous ideals and apply it to classification of configurations of points with minimal or no fattening effect.

article

Reduction of Power Series in a Polydisc with Respect to a Gröbner Basis

Justyna Szpond

Bulletin of the Polish Academy of Sciences. Mathematics > 2005 > 53 > 2 > 137-145

We deal with a reduction of power series convergent in a polydisc with respect to a Gröbner basis of a polynomial ideal. The results are applied to proving that a Nash function whose graph is algebraic in a "large enough" polydisc, must be a polynomial. Moreover, we give an effective method for finding this polydisc.

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Keywords

13A15 (1)
13E10 (1)
13F20 (1)
14C20 (1)
14J26 (1)
14N05 (1)
ARRANGEMENTS OF LINES (1)
ASYMPTOTIC HILBERT FUNCTION (1)
CHUDNOVSKY CONJECTURE (1)
COMBINATORIAL ARRANGEMENTS (1)
CONTAINMENT PROBLEM (1)
CONTAINMENT PROBLEM FOR POWERS OF IDEALS (1)
FAT POINTS (1)
LEFSCHETZ PROPERTIES (1)
LINEAR SYSTEMS (1)
PAPPUS THEOREM (1)
POSTULATION PROBLEM (1)
SHGH CONJECTURE (1)
SYMBOLIC POWERS (1)
TOGLIATTI SYSTEM (1)
UNEXPECTED HYPERSURFACES (1)
WALDSCHMIDT CONSTANTS (1)
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Elsevier (2)
Springer (2)
DML (1)
Wiley (1)

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Search results for: Justyna Szpond

Unexpected curves and Togliatti‐type surfaces

Lower Bounds for Waldschmidt Constants of Generic Lines in $${\mathbb {P}}^3$$ P3 and a Chudnovsky-Type Theorem

From Pappus Theorem to parameter spaces of some extremal line point configurations and applications

Asymptotic Hilbert polynomials and limiting shapes

Points fattening on P1×P1 and symbolic powers of bi-homogeneous ideals

Reduction of Power Series in a Polydisc with Respect to a Gröbner Basis

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