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On Extremal Rational Elliptic Surfaces.

Rick Miranda, Ulf Persson (1986)

Mathematische Zeitschrift

On graded Bett numbers and geometrical properties of projective varieties.

Uwe Nagel, Yves Pitteloud (1994)

Manuscripta mathematica

On irreducible components of a Weierstrass-type variety

Romuald A. Janik (1997)

Annales Polonici Mathematici

We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.

On minimal models of elliptic threefolds.

Antonella Grassi (1991)

Mathematische Annalen

On the (-1)-curve conjecture of Friedmann and Morgan.

Rogier Brusee (1993)

Inventiones mathematicae

On the connectedness of the locus of real Riemann surfaces.

Costa, Antonio F., Izquierdo, Milagros (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

On the difference between real and complex arrangements.

Günter M. Ziegler (1993)

Mathematische Zeitschrift

On the Euler Characteristic of Complex Algebraic Varieties.

Zbigniew Szafraniec (1988)

Mathematische Annalen

On the Euler characteristic of fibres of real polynomial maps

Adam Parusiński, Zbigniew Szafraniec (1998)

Banach Center Publications

Let Y be a real algebraic subset of $^{m}$ and $F : Y \to^{n}$ be a polynomial map. We show that there exist real polynomial functions $g_{1}, . . ., g_{s}$ on $^{n}$ such that the Euler characteristic of fibres of $F$ is the sum of signs of $g_{i}$ .

On the Euler characteristic of the link of a weighted homogeneous mapping

Piotr Dudziński (2003)

Annales Polonici Mathematici

The paper is concerned with an effective formula for the Euler characteristic of the link of a weighted homogeneous mapping $F : ℝ ⁿ \to ℝ^{k}$ with an isolated singularity. The formula is based on Szafraniec’s method for calculating the Euler characteristic of a real algebraic manifold (as the signature of an appropriate bilinear form). It is shown by examples that in the case of a weighted homogeneous mapping it is possible to make the computer calculations of the Euler characteristics much more effective.