Abstract:
Given a pseudo-effective line bundle L on a compact Kähler manifold X of dimension n, it is well-known that the leading order term of dim H^0(X,L^k) is given by vol(L)k^n. When L is equipped with a singular plurisubharmonic metric \phi, it is natural to replace H^0(X,L^k) by the subspace of L^2 integrable sections H^0(X,L^k\otimes I(k\phi)). We show that in this case, the leading order term of dim H^0(X,L^k\otimes I(k\phi)) is still of order k^n with coefficient given by a natural construction in pluripotential theory. This is a joint work with Tamás Darvas.

Speaker:
Mingchen Xia is currently fourth year PhD at Chalmers Tekniska Högskola under the supervision of Robert Berman. His research focuses on pluripotential theory and non-Archimedean geometry.

Zoom:
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