Abstract：Finding the Noether inequality for varieties of general type is a natural problem in the study of algebraic geometry, which dates back to the work of M. Noether for surfaces. Later, Debarre proved that irregular surfaces of general type satisfy a stronger Noether inequality. Recently, J. Chen, M. Chen and C. Jiang established the optimal Noether inequality in dimension three. In this ...
AbstractGeometric inequalities reveal relation between different geometric quantities, such as volume, surface area, width, diameter, etc. By the correspondences between convexity and positivity, such as mixed volumes of convex bodies and intersection numbers of divisors, we present a series of new geometric inequalities inspired by positivity results from algebraic and analytic geometry.Speake...
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