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Abstract: A net is a special configuration of lines and points in the projective plane. There are certain restrictions on the number of its lines and points. We proved that there cannot be any (4,4) n...
Abstract: In 1981 J. Wahl described smoothings of surface quotient singularities with no vanishing cycles. Given a smoothing of a projective surface X of this type, we construct an associated exceptio...
Abstract: We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton...
The k-secant degree is studied with a combinatorial approach. A planar toric degeneration of any projective toric surface X corresponds to a regular unimodular trian-gulation D of the polytope definin...
As a stable analogue of degenerations, we introduce the notion of stable degener-ations for Cohen-Macaulay modules over a Gorenstein local algebra. We shall give several necessary and/or sufficient co...
Let f ∈ Z[x1, . . . , xn] be a non-constant polynomial, and let p be a prime. Igusa’s p-adic zeta function Zp f (s) is a meromorphic function on the complex plane that encodes the number of solutions ...
We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations.
We classify irreducible d-semistable degenerations of primary Kodaira surfaces. As an application we construct a canonical completion for the moduli space of primary Kodaira surfaces.

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