How Long to Read Donaldson Type Invariants for Algebraic Surfaces

How Long Does it Take to Read Donaldson Type Invariants for Algebraic Surfaces?

It takes the average reader 6 hours and 50 minutes to read Donaldson Type Invariants for Algebraic Surfaces by Takuro Mochizuki

Assuming a reading speed of 250 words per minute. Learn more

Description

In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting “universal relations among invariants”, which would be a natural generalization of the “wall-crossing formula” and the “Witten conjecture” for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ̈ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.

How long is Donaldson Type Invariants for Algebraic Surfaces?

Donaldson Type Invariants for Algebraic Surfaces by Takuro Mochizuki is 404 pages long, and a total of 102,616 words.

This makes it 136% the length of the average book. It also has 125% more words than the average book.

How Long Does it Take to Read Donaldson Type Invariants for Algebraic Surfaces Aloud?

The average oral reading speed is 183 words per minute. This means it takes 9 hours and 20 minutes to read Donaldson Type Invariants for Algebraic Surfaces aloud.

What Reading Level is Donaldson Type Invariants for Algebraic Surfaces?

Donaldson Type Invariants for Algebraic Surfaces is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

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