K-stability and birational models of moduli of quartic K3 surfaces
K-stability and birational models of moduli of quartic K3 surfaces
Abstract We show that the K-moduli spaces of log Fano pairs $$({\mathbb {P}}^3, cS)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> where S is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily–Borel compactification of moduli of quartic K3 surfaces as c varies in the interval (0, 1). We …