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Using Tropical Degenerations For Proving The Nonexistence Of Certain Nets
Tropical Degenerations The Nonexistence Of Certain Nets Algebraic Geometry
2011/9/22
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...
Exceptional bundles associated to degenerations of surfaces
Exceptional bundles degenerations of surfaces Algebraic Geometry
2011/9/5
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...
Secant Degree of Toric Surfaces and Delightful Planar Toric Degenerations
Toric varieties secant varieties degenerations polytopes
2011/1/20
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...
Stable degenerations of Cohen-Macaulay modules
degeneration Cohen-Macaulay module finite representation type stable category
2011/2/24
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...
Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties
Motivic zeta functions degenerations of abelian varieties Calabi-Yau varieties
2011/2/25
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 ...
Examples of degenerations of Cohen-Macaulay modules
degeneration Cohen-Macaulay module finite representation type
2011/2/25
We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations.
The degeneration formula for logarithmic expanded degenerations
degeneration formula logarithmic expanded degenerations
2010/12/10
The degeneration formula for logarithmic expanded degenerations.
Irreducible degenerations of primary Kodaira surfaces
Irreducible degenerations primary Kodaira surfaces
2010/10/29
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.