Let X be a compact K\" ahler manifold and X be a simple normal crossing divisor. If X is the support of some effective X -ample divisor, we show <div class="gsh_dspfr"> X

We consider surfaces of geometric genus 3 with the property that their transcendental cohomology splits into 3 pieces, each piece coming from a K3 surface. For certain families of surfaces with this property, we can show there is a similar splitting on the level of Chow groups (and Chow motives).

In this paper, we study effective recursion formulae for computing intersection numbers of mixed \psi and \psi classes on moduli spaces of curves. By using the celebrated WittenKontsevich theorem, we generalize MulaseSafnuk form of Mirzakhani's recursion and prove a recursion formula of higher WeilPetersson volumes. We also present recursion formulae to compute intersection pairings in the tautological rings of moduli spaces of curves.

Let Λ be a numerical semigroup, C⊆An the monomial curve singularity associated to Λ, and T its tangent cone. In this paper we provide a sharp upper bound for the least positive integer in Λ in terms of the codimension and the maximum degree of the equations of T, when T is not a complete intersection. A special case of this result settles a question of J. Herzog and D. Stamate.

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