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In this paper, we consider weighted counts of tropical plane curves of particular combinatorial type through a certain number of generic points. We give a criterion, effectively balancing , derived from tropical intersection theory on the secondary fan, for a weighted count to give a number...
In this paper we prove results on topological properties of quotients of manifolds, in particular of projective spaces and spheres. Specifically, under suitable conditions we exhibit results on homology and homotopy groups of these quotients. As an application we generalize the characterization...
We study two boundary value problems for a surface of revolution moving under Gauss curvature flow. The rotational symmetry allows us to reduce to an equation on the generating curve so that there is no restriction on the sign of the curvature of the initial surface.
We show that for a hypersurface Batyrev's stringy E -function can be seen as a residue of the Hodge zeta function, a specialization of the motivic zeta function of Denef and Loeser. This is a nice application of inversion of adjunction. If an affine hypersurface is given by a polynomial that is...
In Dürr, Kabanov, Okonek, Topology 46: 225–294, 2007 we constructed virtual fundamental classes for Hilbert schemes of divisors of topological type m on a surface V , and used these classes to define the Poincaré invariant of V : We conjecture that this invariant coincides with the full...
A smooth, projective surface S is said to be isogenous to a product if there exist two smooth curves C, F and a finite group G acting freely on C × F so that S = ( C × F )/ G . In this paper we classify all surfaces with p g = q = 1 which are isogenous to a product.
We construct a family of examples of Legendrian subvarieties in some projective spaces. Although most of them are singular, a new example of smooth Legendrian varieties in dimension 8 is in this family. This 8-fold has interesting properties: it is a compactification of the special linear group,...
Given a smooth and oriented surface M in the Euclidean space ℝ 3 , the conjugate curve congruence C α is a family of pairs of foliations on M that links the lines of curvature and the asymptotic curves of M . This family is first introduced in Fletcher, Geometrical problems in computer vision,...
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