On the Minimal Degree of Rational Projections of K3 Surfaces with Low Genus
This paper investigates the degree of irrationality of K3 surfaces with genus up to 14, demonstrating that it is at most 4, and explores the structure of rational maps of minimal degree from these surfaces to the projective plane.
Crepant Resolution of the Quotient Singularity A4/A4 in Characteristic 2: A Counterexample to Batyrev's Theorem
This paper presents a counterexample to the analogous statement of Batyrev's theorem in positive characteristic by constructing a crepant resolution of the quotient singularity A4/A4 in characteristic 2, where the Euler number of the resolution differs from the number of conjugacy classes of A4.
Computing the Intersection Cohomology of Moduli Spaces of Vector Bundles Over Curves Using Donaldson-Thomas Invariants
This paper presents a method for computing the intersection cohomology of moduli spaces of vector bundles over curves by relating them to Donaldson-Thomas invariants, which can be calculated effectively.
Classification of Projective Surfaces with T-Singularities and Ample Canonical Class: Identifying Horikawa Surfaces and Exploring Their Smoothability
This research paper classifies all projective surfaces with only T-singularities, ample canonical class, and K² = 2p_g - 4, identifying all such surfaces (smoothable or not) within the KSBA moduli space of Horikawa surfaces.
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